It might come as a surprise but....we've all been there at some point.
The bit about same enemies is actually something that is MMO based design, Destiny has quite a varied enemy design it's just that for a game like this no matter how varied they are it will feel samey after a time but it's not the point of the game really.
The trick is to find something that you like rather than do everything, you don't do everything unless you are chasing a certain gear or something. I used to play everything, every week...got burned out. Then I only played raids as it was fun no matter how many times I played them because I'd have my own meta game in that I'd try different things (gear combinations, abilities, strategies etc rather than just follow the same routine over and over). Then HoW came out, I played PoE and got burned out of it pretty soon as it was everything that I hated about PoE...it is slightly better now with the removal of burns from skolas, health reduction for Quodron and on some weeks the modifiers on that pilot servitor are not complete shit. Sometimes the meta changes due to weapon rebalancing, which will change again in 2 months time.
Regardless I found my new home in Destiny to be PvP, I may run the odd nightfall once in a while but don't really play PvE anymore. I play Trials every week...for the days I can't I play regular crucible. When Iron Banner comes out I play that....it's the same shit in reality and it's even more limiting because there are far too few maps to play on (especially now that some of them have been removed from the game modes, and some game modes are limited time events) to top it off it's unbalanced and has a LOT of connection issues.....but I still enjoy it. Especially the competitiveness which is what I come back for.
Basically you find something you like for the time rather than try to get yourself to like something you can't (atleast at that moment in that time, you might like it later).