This might seem harsh but often people complain for stuff that didn't actually happen, and this page explains how each player in MTA perceives things slightly differently and how that comes about.
San Andreas was never designed for multiplayer and has no built in way of communicating over the net. What MTA does is override parts of the San Andreas engine - most notably to override the menu, disable pedestrians and other traffic, and add the server browser. In a race, your MTA is constantly sending your car's position to the server, and the server is sending everybody else's cars back to you. MTA then puts these cars into your otherwise empty game as something similar to the AI drivers in races.
The data doesn't travel instantly over the internet. Everybody's car takes a short time to get to the server and then the whole set of cars takes the same length of time to get back. This has the effect that:
This means that if you see yourself side by side with somebody, they see themselves as further ahead, by up to a few car-lengths. They probably have no idea where you are so it's best just to bear this in mind and hang back if your only other choice is to drive alongside them. I always prefer to hang back and pass later when there's actually room.
It doesn't just stop at driving next to one another. You might accidentally bump into someone at your end, but to them they were already past you when you moved out, or you might skim close to someone at your end but to them you give them a bump which ends up in them spinning out.
Another thing that happens if you pull in right in front of someone, is that they might actually be two car lengths ahead and so to them you pull in right behind them. Then when you brake they'll pass right through you smashing you out of the way, because you weren't properly in front of them.
Basically be very careful close up, because nothing will be quite in sync. Always make sure you're well ahead before pulling in front of someone, to be sure you're definitely ahead in both views.
