Dentist recently recommended "crowns" for 2 teeth. What happens if I avoid the crowns? Can teeth possibly get stronger? He said they could break off!

Yes, could break! You don't mention why your dentist recommends crowns for your teeth other than "they could break off". Are there large, defective fillings, is their recurrent decay, did these teeth have root canal, are your teeth already chipping away? All are good reasons to get crowns as treatment. Your teeth will not get stronger on their own, so follow your dentist's advise. Crowns may very well save ur teeth.
Need for a crown. A crown is needed when there is not enough tooth left to hold in a filling. Thus usually occurs when one or more cusps is gone and /or there is less than 50% of the tooth left. More often than not, a tooth does not need a full crown. A partial crown or an onlay is a much more conservative option. Find a dentist that has a cerec, they tend to do more onlays.
Get second opinion. Teeth can't really get stronger. If they need crowns, then they can and may break without them. If you are uncertain, I suggest you get a second opinion from another dentist.
Depends. It depends on why they recommended the crowns. If there is decay then I would certainly get some sort of treatment. However you're going to get differing views, if you have existing fillings or crack lines. I personally don't require my patients get crowns based solely on crack lines and nothing else. So crack lines only...Maybe observe; crack lines with pain...May advise crowns. Get 2nd/3rd opinion.
Crown for teeth. When the tooth is worn out (grinding during sleep, eating too much hard foods.) the outer layer is so thinned out it would not recover and the deeper layer will lose the protection of outer layer. The tooth can be damaged beyond recovery if the crown is not made timely.