The obvious reason is "Anno wanted to do an Evangelion movie", I know.

I saw a lot discussions about the purpose of episodes 25 and 26, while the discussions about the movie are mostly about plot points and characters interactions. I've spent the last few days searching for interview about what exactly pushed Anno and the staff to make the movie without finding anything really usefull.

Has Anno ever explained why the movie was made? In more than one interview he said that the original ending was what he wanted, so why another end?

I think this has always been pretty easy to figure out.

I always got the general impression from his interviews and statements that Anno was "satisfied" with EOTV, not that it was necessarily the one he wanted. There's a big difference in connotation there.

By this point, almost everyone knows that the production schedule towards the end of the series was ridiculously rushed. I'm positive that, although Anno was publicly "satisfied" with EOTV, the wave of popularity that accompanied the ending of the show gave him the opportunity to have the time and resources to execute the climactic JSSDF invasion and Eva Series sequences in AIR25' he had originally planned for EOTV25, as well as being able to make a more "beautiful" version of Instrumentality to end the series, as well as having the opportunity to throw in some scenes to comment on his fanbase (the hospital scene, the thank you/death threat letters).

Also, being able to do a theatrical release would unburden him from TV studio restrictions on what he would be allowed to include. NGE is to Twin Peaks as End of Evangelion is to Fire Walk with Me .