Scientific mind here too. In the legal field - which is unromantic but a good field to study obligations / promises from a scientific viewpoint -, there are two kinds of obligations: the obligations of means and the obligations of result. When you go to the doctor, he has an obligation to diagnose and treat you but that's an obligation of means: he has to apply appropriate medical knowledge and methods - essentially try his best - but the diagnosis could be wrong or the treatment fail through no fault of his and he would have fulfilled his obligation. When you purchase something online, the vendor has an obligation to deliver the thing and that's an obligation of result: he actually has to give you the thing; if he doesn't, he hasn't fulfilled his part and you wouldn't say "oh well, you did your best, here is your payment buddy".

The same can be said for marriage vows. The promise to love him is an obligation of means, you'll try your best. The promise to be faithful is hopefully an obligation of result, you won't sleep with his brother - not just try. For this reason, I don't think it's false to promise to love him; I think one can honestly make that promise and everyone understands it's a promise to try your best, an obligation of means.

That being said, if you don't like it, you can find an alternate wording such as promising to cultivate your love for one another. It's more romantic than "can't promise but I'll try", without promising to love him.