If my memory serves me correctly, I think there was an episode regarding this issue in Seinfeld.
Seinfeld said 'I love you' to his girlfriend, and the girlfriend simply says 'me too', and in the show, it's thought of as the girlfriend not feeling the same way, i.e. she doesn't love him, or that the emotional intensity is low, or that she just wants to pass it by (not fully accept it or acknowledge what she has heard).
The saying 'I love you' is a very important thing to say to someone, especially the first time.. it's a big deal to say this out aloud. But if the other person simply says 'me too', then that's not being appreciative of this fact. To properly and equally convey the fact the recipient feels the same way, the proper thing to say is 'I love you too', because it is more sincere and there's the word 'love' in it, which is very important. So to summarize, the idea is to equally give back, so to speak, and to make it very clear that the other person loves him/her too.
... the preceding was from a non-gramatical viewpoint.