If you haven't seen the episode yet, then please watch it before reading this post. Thank you
Wells/Thawne got visibly upset when he learned Barry hadn't saved his mother and then the two fought where Reverse Flash almost kills Barry (and would have if Eddie hadn't shot himself).
Here's my "theory" on why Wells/Thawne got mad and was all for Barry saving his Mother.
1. We know in the end of the episode, a singularity appears and begins consuming the city. This was a result of Eddie killing himself which resulted in Reverse Flash never existing, which in turn resulted in the forming of the singularity which would probably wipe out the timeline if Barry doesn't succeed in destroying it.
2. Wells/Thawne wanted Barry to go back and save his Mom, but remember Wells/Thawne HATES Barry. I think he had a double agenda here.
3. Let's say Barry DID save his mother by fighting Reverse Flash. Reverse Flash either kills Barry or either Barry manages to get away. Either way, the future Barry knew is gone forever because a singularity would appear over Central City and consume it (and probably the timeline) even as Wells/Thawne makes his get-away with his Time Sphere. Thus, Wells/Thawne gets his revenge.
4. If Barry had saved his Mom then he wouldn't have been able to return to the future because the singularity would have formed over Central City and consumed it and possibly that future. Thus, Barry would be stuck in the past just as Thawne was (or be dead).
I know my theory has holes in it and feel free to poke holes in it. *Laughs* When dealing with time travel, there's bound to be problems, no matter how well one looks at the angles.
And there you have it. That's my theory as to why Wells/Thawne wanted Barry to go save his Mom and then got furious when Barry chose not to do it to the point of nearly killing him.
One final note: Wells/Thawne states he is from 136 years in the future. That would place him being from the year 2151. Obviously the writers didn't do enough research. Eobard Thawne is from the 25th century not the 22nd century. Here's hoping Wells/Thawne was simply lying. And until I see solid proof he wasn't, I'm going to assume he was.
Rather than wonder about Wells/Thawne's issue with Barry saving his mother I'm wondering what now? Eddie kills himself thus erasing the Reverse Flash from being born....so wouldn't that erase the real Wells from dying and the progression of S.T.A.R. Labs and the particle accelerator....erase Barry becoming the Flash OR, reaching back more, Barry's mother being murdered so....essentially, while all the players would exist today (though Barry wouldn't be The Flash and who knows if Cisco and Kaitlin would be associated with S.T.A.R. Labs since they were hand-picked by Well's/Thawne NOT the real Wells) where are we going to be and what will exist and remain in the story?
Those are the thoughts I am having. The ONLY card I wonder about is the one played very quietly between Wells and Cisco but I sense for good reason....Cisco's ability to see between timelines! I mean, SOMEONE in the mix has to know what is and should be..right?