YOU PUT 44 IN YOUR TIRES? That's the MAXIMUM PRESSURE. You're lucky your tires don't explode. You are supposed to put 33 in the tires, the light goes on when it reaches more than 80% of the recommended pressure.
If 44 is the published maximum, than you don't have to worry about something like the tires exploding, unless you had a mis-matched rim size.
Excluding structural defects, tires will explode from under-inflation. Tires heat up as they roll across the ground, and to be specific, it is generated at the two leading and trailing edges of the contact patch in each tire. It is at these two points where the carcasses bends, thus having heat generated from friction. The softer the tire, the greater the flex, the greater the heat.
Why is this important to know? Well if you do a lot of sustained highspeed travel, lets say highway commutes, you would do well to ensure the tires are properly inflated for safety. If you had severely under-inflated tires, you are at high risk of blow-outs, especially on the highway (you generally don't see it happen in low city speeds)
Inflating a tire to it's maximum psi ratings is useful when you are carrying a ton of weight around, otherwise all it will do is lead to reduced traction, harsher rides. The tire simply cannot deform enough to properly grip the surface as well.
A tire exploding off a rim from over pressure would certainly be an issue if you had it comically overinflated.
I had one instance, where our group (motorbikes) filled up/checked pressures before a day of hard riding in some mountain roads. While on the ride, my bike felt unusually rough at the back end.
Out of tight, low gear/high lean angle turns the rear kicked right out as if I was trying to steer with the throttle but I wasn't trying to. I had to stop and check. Turns out my air pressure gauge failed and I had about 50psi (typically want about 28-30). There was no danger of the rear tire expoding, just a very high chance of wiping out because the rear had absolutely no traction.