Why don't they want to get hailed to JFK?

Long drive, capped rates as already mentioned. Also once there you cannot immediately pick up another passenger - you have to go to the central "taxi pool" where you get to line up with dozens/hundreds of other cabs for the privilege of picking up a fare.

So as a driver your choices are to wait forever in a line to pick up a fare from the airport, or beeline it back to Manhattan as quickly as you can with an empty car. Neither are great choices.

Although in the wee hours (between 1 and 6AM), getting a hail to JFK is not bad, because it only takes ~20 minutes to get there, and yields a $60 fare. But during rush hour, getting stuck going to JFK is the worst thing possible, as you lose ~2-3 hours of the best fare times.

Which is why you should use the AE/Penn Station train during rush hour (it'll be faster than a cab), or tip your cabbie very well (30%+), though it still ends up being sucky for them and stressful for you.

Certain destinations (outer-boroughs) will earn you a "shorty" that lets cabbies skip the airport taxi pool lines. Most cabbies prefer this scenario.

It's a long drive (from Manhattan) and the airport rates are capped around ~$40 or so.

Damn, I wish we had that in the Bay Area. I usually take Uber or another black car service from SFO because to Oakland in a taxi it's $90+ on the meter and lots of extra fees.