You don't get it, the issue I have with that scene is this.
Why would Snyder choose to even have Superman call Martha's name? Why not have him say "Save my mom"?
Because they have the same name, and them having the same name is part of the scene. It's an interesting coincidence, and rather than dump all the info about what is going on at once, because it's a film, the writers chose to parcel the info out in what is me ant to be a slow burn sequence.
And because they wanted to have Lois reveal that Martha is his mother.
And because the coincidence of their names being the same triggers Bruce, and reminds him where he came from.
It's a fictional story. Characters don't always do the most prudent thing. Sometimes writers have them do the thing that leads to the most drama.
Someone is about to kill you, you're not gonna say "save Martha!" you'll probably say something like "Please save my mother" or "save my mom"
The obvious answer here is: How is Batman going to know who he's supposed to save if Superman says is "Save my mom" and then Batman kills him?
Beyond that, people don't seem to dislike the scene because they said "Martha" instead of "my mom". People mock the fact that their mothers have the same name and for some reason that coincidence is something to be ridiculed.
This is how you connect to people in that moment. Hell most of the audience had probably already forgotten that Bruce's mom's name was Martha. This was just a poor decision.
Now wait a minute. It's not like the scene doesn't end with us realizing that "Martha" is Clark's mother. The subtext of "save my mom" is very much in the film once Lois shows up, so if people are going to connect to that, then shouldn't they have connected to it anyway?
Snyder goes out of his way to have Superman refer to his mother by her first name in this situation, something people rarely do, something that is rarely seen in other movies. The norm is to call your mother "mom" It's what's been set up in that world as well.
Because it's rarely seen in other movies or rarely occurs in real life, it's wrong? What kind of creative logic is that?
Because it's not the norm, then it follows that Clark thinks that the name "Martha" is important for Bruce to hear. Maybe he doesn't want Bruce to KNOW Martha is his mother, because then Bruce, who has a bone to pick with Superman, might not want to help in that instance.
Or maybe he's, I don't know, dying from Kryptonite poisoning and that's all he can think of or remember after who knows how many blows to the head, beatings, falls and poisonings, that her name is Martha.
Why in MoS did Superman not say to Zod "You think you can threathen Martha!!!" as he was tackling him? because it's weird.
Because it's not about how he addreses her as her son in BVS...it's about getting the specific info about her name to Bruce.
Superman did not need to tell Zod that his kidnapped mother's name was Martha. He needed to explain to Zod that he was pissed off that he dared to threaten his family. Entirely different scenarios.
It's weird and people should just acknowledge that it's weird. Instead of being shocked that people are confused about the scene or disliked it.
A lot of things are weird. A guy dressed in a bat costume killing a superpowered alien with a spear made out of glowing green rock is weird.
Being weird does't make something an invalid creative choice.
I should point out that while there's a vocal section of the audience that hated and ridiculed the moment, it did work for many as well. The moment did not work for everyone, but it is hardly universally hated.