The first problem with this theory is that Harry's behaviour doesn't match that of the only other example we've seen of a character under the influence of a love potion - Ron after eating the spiked Cauldron Cakes. At that time, Ron acted obsessive and out of character. Harry, on the other hand, acted like himself while developing feelings for Ginny. He was able to focus on other things and fought against his feelings for most of the year, worried over how Ron would react. Surely under the influence of a love potion, he would tell Ginny how he felt immediately without considering any consequences. Harry was also able to notice that Ron was acting differently and guess that Ron had consumed a love potion, while no one suspected any such cause for Harry's behaviour throughout the year. If Ginny had used a love potion it'd have likely been one purchased from the twins, and would have had a similar effect to the one used on Ron though maybe slightly less strong due to being consumed earlier.
The second problem is Harry's ability to break up with Ginny at the end of his sixth year. He does this because he fears that Voldemort and the Death Eaters could target her to hurt him. Under the influence of a love potion, he would have been too obsessed about being with her to think that rationally and place her safety above the continuation of their relationship. He wouldn't have been able to focus on the Horcruxes hunt and the wider war against Voldemort at all. Ginny doesn't argue against the break-up either. She understand his reasoning and says that his heroism is one of the reasons why she loves him. This doesn't fit with the actions of someone willing to use a love potion to get someone to date her.
The third problem is Harry's continuing feelings for Ginny during Harry Potter And The Deathly Hallows. She isn't with him, able to theoretically continue giving him a love potion, but he still misses her and looks for her on the Marauders' Map. We learn from Merope Gaunt and Tom Riddle Senior's history that a love potion's effects wear off if not replenished. Harry is very unlikely to still love Ginny, later marrying her and having children together, if a love potion wore off and he learned that's how their relationship started. Ron wouldn't continue to give a love potion on Ginny's behalf because he disapproves of her dating at all and only grudgingly accepts the relationship. He also wouldn't be able to do so after he left. Hermione wouldn't give Harry the love potion because it's likely that she would see the ethical issues with doing so.
The final problem is how this theory conflicts with the wider themes of the Harry Potter series. The story is all about the power of love, from Lily's sacrifice saving Harry as an infant, to Harry's own love protecting him from Voldemort's attempted possession, to Harry's love for others enabling him to willingly sacrifice himself to destroy the Horcrux within him. The idea that Harry's main romantic love was a falsehood caused by a potion, and that this is never discovered and never has any consequences, would be a complete anathema to this theme of love.
