there is nothing that makes you feel more like a man than pumping a smoking husk of a shell out of your shotgun after blowing the living hell out of a paper target!
Uh, okay...
Anyway, I'd say that the pump has many advantages over a semi.
1. Pump doesn't jam with light loads or when dirty (unless REALLY dirty)
2. Pump is inherently safer; without fumbling, you can open the chamber and keep the gun from discharging, and fully unload it with little effort. When it's open, it's obvious from all angles.
3. Pump needs cleaning less often, and it's less work to clean it when you do. (Benelli semiautos are an exception, or at least they stay a lot cleaner and are a lot simpler than gas-operated semis)
4. A good, reliable pump is readily available brand new, Made in USA, for low $200s to low $300s.
5. Shucking a pump shotgun is pretty easy to do fast. Takes a lot less effort and practice than shooting a lever or bolt gun fast.
6. Pump guns are typicall a little lighter. When you use them for hunting, or add a lot of heavy tactical goodies, lighter is better!
7. You can swap barrels from NFA 10" to 34" for geese without any worry about feed problems and no modifications, adjustments or tweaks of any kind.
8. Folding and collapsible stocks, as well as short youth stocks go on all pumps. Some semis have buffer tubes and springs that extend into the buttstock, limiting your options significantly.
The semi has a few things going for it, though.
1. Multiple shots with no pumping.
2. Lower recoil (except Benellis without add-on features; you have to pay the price for easier and less critical cleaning
somewhere, right?)
3. More options for where you can put your forward hand. This can be a HUGE advantage for hunting and clay shooting, a lot more than it would sound like.
Semis are great if you need what they have to offer. Pumps aren't "better." But they can be a better choice.