Berlin defense

I was trying to analyze it with the engine end it seems that white can avoid the endgame and draw by repetition by just playing 5.Re1 instead of 5.d4

Am i wrong? If not, are there other reasons why the Berlin is so annoying for white and some plays 4.d3?

Re1 repeats how? Sometimes the computer will repeat in silly positions where human opponents won't.

The Berlin Defense is a solid way for black to play and that makes it annoying for white to push their advantage into a win. At the higher levels, this opening is drawish and so black often uses this to draw, whereas white wants to win, but it's difficult to prove a win. I share a bit more in this video (more from the black side, but also sharing ideas for white)

Let me rephrase my previous message.

"Re1 avoids the Berlin endgame and it also avoids the draw by repetition"

Re1 still leads at an equalish position; the queens are still on the board, but arguably not much different. Here's one sample line: