untilted

Physics does are about the direction of time: https://en.wikipedia.org/wiki/T-symmetry

An electron is a truly elementary particle. This means that in an e-e collision, you know precisely the center-of-mass energy of the resulting interaction. A proton, on the other hand, is not a fundamental particle: it's composed of quarks and gluons, so even if we know that the proton's energy is 7 TeV, we don't know which fraction is carried by each of the proton's constiuents. And since interactions happen between the constituents, the center-of-mass energy is not fixed, and generally not known with high precision.

It's therefore much better to probe for unknown phenomena using a hadron collider (e.g., a proton-proton or ion-ion) since with a single beam energy you can potentially produce interactions at a wide range of center-of-mass energy. However, if you know the center-of-mass energy of the processe(s) you need to study, a lepton (e.g. electron-electron) collider is more suitable since you can precisely tune the center-of-mass energy of the interactions.

It's also possible to collide electrons with protons. This was done for example at the HERA collider at DESY in Hamburg in the 90's/00's to study the inner structure of the proton.