“sorry, I screwed up. Excuse me. I just need to slip in there.”
My problem with this is that the screw up is the slipping in. In other words, accidents happen and there's nothing wrong with apologizing for something you already did by accident -- but in this case, it's preemptively apologizing for doing something on purpose that you know is wrong, cutting someone off because you already were late/past where you need to go.
If you cut someone off because you didn't see them and you thought it was safe, that's a good reason to apologize. Mistakes happen and it's good to take accountability.
If you're seeing that it's not really safe and the other guy is going to have to slam his brakes because you're going to consciously on purpose cut him off, then yeah you're just being a shitty driver on purpose. Apologizing for something you knowingly did on purpose and will do again? That just makes you a liar on top of that.