is it allowed to use photoshop in logo making?

why do most people prefer coreldraw or illustrator? is it easier to use or it has an advantage over illustrator?

There are tons of tutorials on line to learn vector programs. You can just go to youtube or places like vectortuts, pixel2life, etc...

As long as the logo is vector, you can use photoshop, though it is not recommended. Photoshop is great if you want to do mockups in your logos! I prefer to use Adobe Illustrator.

why do most people prefer coreldraw or illustrator? is it easier to use or it has an advantage over illustrator?

Most people prefer CorelDraw because it has easier learning curve (at least I believe so).

Also, some actions that people usually do in AI, require more fiddling with tool switching and stuff, compared to same when you work in Draw (again, my personal thoughts - some might like this "complexity" ).

Illustrator <3

Maybe not.