A friend of mine in Norway shared some anecdotes of his stint in the Norwegian Army as a tanker. Some of his other friends were surprised by how fragile tanks really are; I wasn't. Tanks are a very, very specialised vehicle, and for the thing they're designed to do, they're excellent. That, however, translates into a lot of weaknesses.
A tank's primary objective is to remain mobile. This means a balance has to be struck between enough armour to keep the squishy humans within undamaged, and little enough armour that the blasted thing can still move for the weight of it. This also means they have to make the main gun as light as possible; and this led to a situation where my friend's squadmates wrecked their main gun by running into a tree. The tree was also destroyed, but the gun was the main problem - and it took three weeks to replace it. This is why the easiest method of removing a tank from a battle is to target its gun; dent the barrel, which isn't that hard, and it's disarmed. No main gun means it's no longer an effective fighting unit. Armouring the main gun sufficiently to prevent this would also prevent the tank from moving around enough to stay alive; surviving a shell hit is one thing, but being able to move fast enough that your enemy can't reliably hit you is quite another, and more effective in the long run.
The other major weak point is the tracks. Tracks are a complicated system, and if you break even one part, the tank's immobilised. A stationary tank is easy to avoid and can be beaten down from outside its range; a mobile tank is far harder to hit. So you try to destroy the track, and that gets you what's known as a "mobility kill"; the tank is immobilised, and rendered far less useful.
And the complexity of tracks is why tanks don't move under their own power unless it's absolutely necessary. All armies which have tanks also have tank transports, which move the big beasts as cargo. A system with as many moving parts as a caterpillar track, in as hostile an environment as the underside of a tank, will wear out very rapidly. Since you need it for the tank to perform its mission, you transport the tank to as close as possible to the front lines and then unleash it. Service intervals on a tank are very short, on the order of hundreds of miles (compared to the thousands of a typical car) because there's so much load on such complicated systems.
Then there's the issue of armour. I mentioned that there's a compromise, and it's worse than you thought. Most tanks have the engine mounted in the rear, partially so the main bulk of the tank is between the engine and the incoming fire, and partially because there's actually very little armour back there, and the engine block can save lives by being in the way should the worst happen and the other lot get a shot at the back of the tank. There's also less armour on the sides, and very little on top. If you want to get through the armour of a tank, go in from above; the natural enemy of tanks is plunging artillery fire.
So while it might seem like a compliment to say that a car feels like a tank, what you're actually saying is it's overcomplicated and a nightmare to maintain. My car is very much unlike a tank, and I'm glad of it.