no one asked for this but
i just had this idea about data and his emotions and i just had to talk about it.
so my personal theory/headcanon about how emotions work for data is that he does have them - they're just very low-volume, for lack of a better expression.
now i know the entire tng fandom has been knew about that for a long time, but i would like to add something to it.
i saw a comment on another post that said that they believed emotion was an essential part of sentience and that got me thinking:
clearly dr. soong can incorporate emotion directly into his androids' systems like he did with lore, but he was afraid that if he did that with data, he would end up like his brother. however, i believe that some emotion is required to create a sentient android - so soong essentially had to figure out the lowest "volume" of emotion to program into data to make him sentient, but hopefully prevent what happened with lore.
so basically my theory/headcanon is that data definitely does feel, but it's just on such a low frequency that he can easily dismiss it as part of his programming. sometimes, he experiences a strong enough emotion that we get to see it sort of surface in barely formed facial expressions and the actions he takes to help those he loves (because yes, data, you do love, you just show it more than you actually feel it).
i don't think he's lying/in denial about his emotions - not really. he can't really feel his emotions very strongly and sometimes he doesn't feel them at all. but, they are there - and when they're strong enough they do surface - but, due to their relatively low volume, it's easy for him to dismiss them.
anyway, somebody's probably already talked about this and i'm way late to the party, but i thought i'd throw in my two cents.