I was participating in a tourney and accidentally closed Toribash. I accept that you cannot be re-entered unless you ping, but I want to know why that is.
Is it a rule having to do with security? Somehow others could enter the tournament if that was allowed?
Please explain this to me.

When you ping it means that your internet is not working properly at that time or something along the lines of that, allowing you to re-enter since it supposedly not your fault. But people use the ping system to their advantage and pinging when they are about to lose so they can re-enter.

If you see anyone doing that, report them to a GM.

Well, sometimes the staff members quit because you're going to lose basically,also this goes with ''GmTourneys'',Rbtourneys,Etc,but these and different tourneys I just told you, since i'm a nice a guy,i'll tell ya rules for it, no spam, no marketing, no in-game links,no back-seating moderator (means a regular players tells a staff member what to do),no Flaming,if you ping in the tourney tell me what it was (the staff member who is hosting it or member of toribash), if you ping during a match you automatically lose and if you see someone doing that screen shot and pm a gm. Does this help or if no pm me

If I accidentally closed the game while in the queue how come I cannot be re-entered?

When you ping, you are able to rejoin primarily because interruptions in your internet connection happens all the time for various reasons, most of which are beyond your control. If you accidentally close the program, you are technically quitting, and leaving the room of your own choice. You aren't allowed to rejoin when you accidentally close the program because the likelyhood of you actually doing that on accident is far less than doing it on purpose, whereas pinging is a different case altogether.