As with most things in life, there is no such thing as a free lunch.
People like 3 under because it eliminates some errors that could be made when shooting split fingers. When shooting split fingers, the forefinger can press down on the nock of the arrow and cause the arrow to bend and rebound off the shelf. Since this is unlikely to be consistent, erratic arrow flight can result.
People like split fingers because it gives them more control of the arrow. You can shoot with a really loose arrow nock and the arrow won't fall off the string. A lot of people who shoot 3 under feel that they need a nock above and below the arrow since there is nothing to keep the arrow from sliding up the string when it is shot. The general feeling is that bows shot 3 under are noisier, even if they have been tillered to shoot 3 under.
Some people have a higher anchor when shooting 3 under, and prefer that, and some prefer a lower anchor when shooting split fingers. I have found that there is a lot of leeway in selecting anchor positions, and not much difference between 3 under and split if you experiment with different anchors.
Some feel that split fingers is more traditional, and some tournaments require that it be used. Not many, though.
If you know how you're going to be shooting, you should obviously have the bow tillered that way. However, most bows can be shot either way without a problem. I have had some bows that were tillered for split where I have had to nock too high and I felt uncomfortable shooting them 3 under, and have sold those bows. I don't know if anyone has bought a bow tillered for 3 under and had a problem shooting it split. Most people who shoot split won't buy a bow that is tillered for 3 under if they know about it, since most bows are tillered for split anyway, and there is no need for them to buy one tillered for 3 under.
I would imagine shooting with two fingers like your dad did would be preferable to shooting with three, if your fingers could stand it. Since almost all people shoot with three fingers, I would assume the average person needs three fingers to comfortably pull the bow.
My perception is that a lot of people switch from split to 3 under, and not many of them switch back (I personally haven't heard of any switching back, but some probably do).