Okay, so before I even start this, I'm going to say 3 things:

1) THIS CONTAINS SPOILERS!!!!!!!!!!!!!!!!!!!!! Just a warning! :)

2) This is totally biased because Percy always annoyed me in the first series (I know, I'm a freak for saying that and I have no logical explanation for it...I always loved Annabeth and Grover more than him...it's weird but true).

2) These are just my opinions and please don't get mad at me for them! :) Thanks. But also, please share your opinions in the comments (but please be nice).

Sooooo, here are my thoughts on why Jason is actually really awesome, even though so many people seem to hate him.
These are things I've read on the internet that people say about Jason that I, personally, find a little ridiculous:

1) "Jason is dull"
I think this is a matter of what kind of characters you like to read about. Jason is serious, not dull. He doesn't crack jokes all the time and say hilarious things like Percy. But he does have his few funny moments (not many, I'll admit)

2) "Jason is a gary-stu"
Okay, I can see where this is coming from. Yes, he seems a little "perfect" in many ways: he's supposedly handsome (at least according to Piper, Aphrodite, and even Annabeth in the first chapter of the Mark of Athena), he's a good fighter, he's powerful...then again, so is Percy. So how does this make him a Gary Stu exactly? I've heard a lot of different arguments on this. Some people say a Gary-Stu/Mary Sue is determined by how the characters see them and not the reader. You definitely can't say that every character in the story thinks Jason is perfect and has no flaws. Yes, certainly Piper does, but can you blame her if she's in love? But Annabeth states multiple times that she still isn't sure she trusts him. And even in the first book, Leo and Piper worry that maybe he really is an enemy, before they know about Camp Jupiter. They don't see him as completely perfect or anything, at least not all the time.
Sorry, I don’t really know enough about a Gary-Stu/Mary Sue to argue this effectively, but that was my best shot! XD
Oh, but also, it doesn't seem like Rick Riordan is the type of author to write a Gary Stu. I mean, all authors make mistakes and it's definately possible, but I just don't think Jason is one.

3) “Jason is a cheap copy of Percy”
I haven’t seen this argument a lot, but I’ve seen it a few times. And I have LOTS of arguments for this one!
1)    Jason and Percy are nothing alike: Percy is hilarious, brave, and a totally impulsive. Jason is serious, brave, and likes to think things through and have a plan. The only thing they really have in common is bravery, which, um, HEROES ARE SUPPOSED TO BE BRAVE! XD Leo is brave, Frank is brave, Annabeth is brave, Piper is brave, Hazel is brave! Okay, sorry, I’m done with that now!
2)    If Jason was REALLY a copy of Percy, why would people hate him so much? If you love Percy and Jason is so much like him, shouldn’t you like Jason too? Okay, that doesn’t make as much sense as I originally thought, but to an extent…
3)    Rick Riordan is a brilliant author who knows how to write AMAZING characters. It’s obvious that he loves Percy, so why would he try to make a cheap copy of a character he cares about so much? Riordan wouldn’t write a Percy rip-off, it just wouldn't make sense. If he was going to rip-off a character, wouldn't he choose one that he doesn't care about as much? I don't know, maybe that's not true, but I think Riordan really loves Percy.

4) “Jason is a player because he is dating Piper”
Oooookay, the definition of a player is someone who tries to be with/is with more than one person/likes a bunch of people and flirts with a lot of people (yes, I know that’s not the actual definition, but it’s the general idea). Jason is the EXACT OPPOSITE of that. He NEVER liked Reyna (as far as we know and as far as Jason has let us believe so far) and THEY WERE NEVER DATING. He is with PIPER and Piper alone. Not Piper and Reyna. He didn’t lead Reyna on. It’s not his fault if he doesn’t love her. In a perfect world, the person you like would like you to. But that doesn’t always happen. It’s unfortunate for Reyna, but it is NOT Jason’s fault. He shouldn’t be with her if he doesn’t love her. That wouldn’t be fair for either of them.
Oh, and can I just point out that if ANYONE is a player, it’s Reyna. She “hit on” (not really the right way of putting that but…) Percy when Jason was missing. Yes, you could argue that she didn’t know if he was ever coming back, but clearly she still hoped he was. So if anyone can be called a “player” it’s her, not Jason. But honestly, neither of them are. They’re both great, in my opinion.

5) “Jason is a jerk”
How so? I can’t really remember many times when he was a jerk, whereas I can think of PLENTY of parts when Leo was a jerk (don’t get me wrong, I absolutely LOVE Leo! I’m just saying that he’s more of a “jerk” than Jason is). I’ll name 2 parts that I can think of when Jason was a jerk.
1)    When he asked Reyna if he could show Piper around New Rome. Did he do this intentionally to be a jerk? Doubtful, but possible. I really don’t think so, I think he was probably just oblivious, but we don’t know since it wasn’t from his point of view.
2)    When he was reluctant to go save Nico. But did he have a legit reason for this? Yes. Is it still rude considering he’s Hazel brother and Hazel is Jason’s friend? Yes. But he DID apologize for this one.
I honestly can’t think of any other times when Jason was a jerk. I mean, he’s not always SUPER friendly, but no one is. Not even Percy, guys. If someone can tell me exactly WHY they think Jason is a jerk, I’d be happy to try and debate it in a mature manner, but I can’t think of any other times. Then again, it’s been a while since I reread the first book, so…

6) “Jason is trying to be better than Percy”/ “Jason is trying to take Percy’s place”
This one seems a little ridiculous to me. Because 1) in The Lost Hero, Jason didn’t even KNOW Percy. He knew who he was and he knew that he was epic, but he didn’t know much more than that. How can Jason possibly have been trying to take Percy’s place or be better than him? And 2) in the Mark of Athena, Percy and Jason were BOTH trying to be better than each other. It’s just natural. Both leaders, one Roman one Greek…clearly they are going to be a little jealous of each other sometimes.

7) “Jason took over Camp Half-Blood and that’s SO not fair, he doesn’t deserve it!” (I haven’t actually seen this argument worded exactly like that, but that’s a summary of it XD)
First things first: Jason DOES deserve it. He saved Hera and therefore, Camp Half-Blood. And also: he’s the ONLY CAMPER in Cabin One. Of COURSE he’s going to be the head counselor.

8) “Jason is not very Roman”
The reasons that were given for this argument were: 1) he put Piper ahead of his duty and 2) he wouldn’t mind leave Camp Jupiter to go to Camp Half-Blood.
I disagree, saying that he is VERY Roman. Jason puts his duty before almost anything else. However, Piper is his girlfriend. He SHOULD put her ahead of his duty. It’s called being a gentleman. And as for him leaving Camp Jupiter for Camp Half-Blood, well, let’s face it guys, Camp Half-Blood is PROBABLY a lot more fun. XD And if he truly loves Piper, he would want to be with her. What’s wrong with that? That doesn't necessarily make him un-Roman, it just makes him a good boyfriend.

9) "Jason is TOO Roman"
Yes, I've seen this argument AND the one above. Awkward?
And what's wrong with Jason being Roman? Um, he IS Roman! XD So what if he's serious and stuff like the Romans at Camp Jupiter are? That's the point. Percy = Greek. Jason = Roman.

10) “Jason didn’t even greet his friends at Camp Jupiter, he’s such a mean person! He doesn’t even care about his home and family!”
Uh, I have a few arguments for this, but some of them are just theories more than fact.
Here’s my actually factual one: There wasn’t much time for Jason to hang with his old friends! The meeting didn’t go quite as planned, remember?! :P
Now for my theories:
1)    Jason has said more than once that everyone at Camp Jupiter expected a lot from him because he is a child of Jupiter. Maybe he didn’t really have many ACTUAL friends? Maybe he never felt very close to anyone (besides Reyna, of course) because they all sort of…I don’t know, put him on a pedestal or something? (Yes, I know this probably isn’t true, but it’s just a thought that I had…)
2)    Jason isn’t very open with his feelings. We’ve definitely seen that. It’s probably why everyone always complains that he’s “stiff” and boring. But maybe he didn’t say hello to any of his friends because he’s just not the type to get all emotional with greetings and stuff. Just a thought. :)
Okay, and the other thing that I have to say about this one:
    Jason may have been a little rude to not say hi to his old friends, but they freakin’ attacked him. Someone threw a BRICK at him (well, technically Piper, but still, they ignored him when he kept saying “I’m on your side!”). Is that how your friends/family should greet you after you’ve been MISSING?! Yes, I get it that Jason came with the Greeks who, in the Romans eyes, attacked them, but still, don’t they owe it to their old Praetor to be a little nicer? So it wasn’t JUST Jason. It was also the rest of the Romans.

11) “Jason is SO conceited!”
How on EARTH (or should I say Gaea? Okay, sorry, bad joke) is Jason conceited?!?!?!? There are MULTIPLE times in the books when Jason says/thinks that he isn’t sure of himself. He even admits to Piper that he thinks he doesn’t deserve her and that he wouldn’t have been brave without her. That doesn’t sound very conceited to me!! XD
Also, I can see how Jason would appear CONFIDENT. But, that’s called bravado, people! It’s when you FAKE being confident. Percy does that too!

12) "Jason is whiny and moody all the time"
Jason doesn't really ever "whine". At least not that I can recall. He may have complained a few times about having his memory taken away, but so did Percy and who wouldn't??? Other than that, though, when does Jason ever whine? And actually, when is he ever moody? Maybe I just missed something huge while I read these books, but I dont' remember him being exactly moody...

Wow, okay, sorry that was SOOO long. I didn’t plan for it to be! But, yes, after all of this I hope that I have convinced a FEW Jason-haters at least that he’s not SO bad! He’s actually pretty awesome!

I don’t blame people for not liking Jason as much as Percy, because let’s face it, Percy has been in WAY more books, so he’s grown on all of us. But give Jason a chance. He’s really awesome!!!! :)