but not always

I'll gladly give you my input about pitching from different sides of the rubber but ultimately you will have to decide what works best for you and where you are comfortable. There are many baseball theories on this but ultimately you will have the final say because you are doing the pitching.
Usually, but not always, a right-hander stands on the third base side of the rubber and a left-hander on the first base side. Many believe this method gives you a better angle to the hitter. Let's use a right-handed batter against a right-handed pitcher as an example. The righty pitcher who is starting from the third base side of the rubber will create the effect that the pitch is coming toward the righty batter and then going over the plate. If the righty pitcher is on the side of the rubber closest to first base, the righty batter will possibly be a little more comfortable. The reason is the ball is starting away from him and then coming into the plate.
Now, it can get a little tricky. Many pitchers who have a tail on their fastball, will do the opposite.
If that's the case, the right-handed pitcher usually will opt for the first base side of the rubber and the left-handed pitcher will usually opt for the third base side of the rubber. Once again, it will give the pitcher a slightly better angle to the batter.
Some left-handed pitchers will pitch on the first base side of the rubber to left handed batters only, to make it even more intimidating to the batter.
Some right-handed pitchers will do the same and stand on the third base side of the rubber for right-handed batters, to make it more intimidating for the right-handed batter.
The point here is that there is nothing etched in stone as to where any pitcher should stand on the rubber.
I do however, think it makes a lot of sense for a right-handed pitcher to stand on the third base side of the rubber when facing a right-handed hitter and for a left-handed pitcher to stand on the first base side of the rubber when facing a left-handed hitter. As a pitcher, isn't it your job to make hitters uncomfortable? I truly believe that it's your job. Hitters should never be too comfortable when facing you. If a baseball hitter is intimidated by a pitcher, half the battle is won by the pitcher before the battle even begins!
It's your shot to call on this one. Baseball pitching tips quite often include experimentation and finding out what works best for you.