I've always seen everywhere that Lorentz transformations are rotations in 4D. Let's stick with 2D (one space axis, one time axis) for simplicity.
Rotations of two dimensional space axes look completely different from the 2D Lorentz transformation. To rotate space axes, we rotate both x and y axes by an angle of same magnitude with same sign. This results in the axes still remaining at 90 degrees after the rotation.
But Lorentz transformations in 2D look like rotating both space and time axes by an angle of same magnitude but opposite signs. The axes don't remain at 90 degrees after Lorentz transformations, instead they form a V-shape. How is this a rotation? Are we using some generalised definition of rotation? Also, why not just rotate both space and time axes in the same direction (so that they remain at 90 degrees), like we do with two space axes? (I've read the reason we don't treat the time-axis like a usual space-axis is that we can't move backwards in time. If this reason is correct, then please elaborate on this. How does rotating both x and t axes in the same direction mean we are going backwards in time?)
EDIT- https://www.mathpages.com/rr/s1-07/1-07.htm I'm coming off this text. Near the end of the first paragraph, it says that the reason we choose to do the 'opposite sign' rotation is that we can't go backwards in time.