Because it would be inappropriate? Because there are laws against public nudity? Because only your husband/wife should see you in your underwear? Because you don't want anyone to see your fat?
If you wouldn't wear your underwear in public... why would it be okay to wear a swimsuit to the beach?
I have, in fact, seen swimsuits that are MORE revealing than underwear... so why are people wearing them?
Here's what God has to say about modesty: 1 Tim 2:9 In like manner also, that women adorn themselves in modest apparel, with shamefacedness and sobriety; not with broided hair, or gold, or pearls, or costly array;
Considering those instructions for women, is a swimsuit in ANY way modest?
I was saved for around a year before our pastor made a comment that got to me... he said "If you wouldn't wear something in church, why would you wear it elsewhere?"
My first response was "But the BEACH is different" as I'm sure someone else is thinking right now. You wear the appropriate dress for a location, right?
So who says it has to be practically naked?
Everyone's definition of modesty is different... to swim, I would wear a one-piece swimsuit (with no chest showing) and board shorts.
I just try (put some pots out to catch the sarcasm here) not to worry about my tan lines... And as for my three girls, they wear rashguard now - not "cute" little baby bikinis. They're going to have plenty of time to fight off the world trying to sexualize them... I think I'll give them a break for now.
I couldn't post of picture of the little girls in the bikinis... it just makes me sick. Go here if you're trying to convince yourself it's cute. It's not. It's exploitation and sexing up BABIES. The porn industry has enough business without our contribution. Trust me.
In addition to modesty, worry about the example you're setting for your children, the stumbling block you would be to other Christians and the testimony you're giving to the unsaved.