monster walking

I've always noticed that enemies don't like going down stairs that much they would simply walk near the linedef and sometimes cross it but it would take awhile. Why is this?

Possibly the stairs are too steep and the steps are not thick/wide enough, and the monster is wide. Like the demons in E1M9 don't want to come the last step down to the room. Some ports have some settings that can allow them to move more freely, which makes things a bit more interesting.

I usually do stairs with this kind of settings: 8 height, 32 thick. 16 height, 64 thick. 24 height stairs I don't really use, except maybe as fake ladders for player, which monsters might avoid with those movement settings too.

The engine figures the depth of step for the next movement and compares it to a max for that monster. When the steps are narrow this may or may not involve crossing more than one step, and thus it critically depends upon the monster distance from the stair step.

Monsters might not go down steps that they easily went up.
Add another tread to reduce step height, and few odd height steps (a few 7 instead of all 8's) make the height checks pass more often when it is close to the monster limit and 3 steps are involved.
It makes a big difference if the monster has only 2 steps to cross or it there are 3 or more steps involved. A larger monster tries to take them in one large step and can cross multiple steps. If they happen to only cross 2 steps, they will likely get stuck halfway up the steps where they cannot cross the next 3 steps.

See the section: Monster sizes and usable steps
in http://doomlegacy.sourceforge.net/hosted/level_design_r3.txt