First caveats:
Most people carry right front pocket so common arguments are with respect to that method. Any other way you carry could work differently with different clip positions. Reading these threads over the years it seemed that half the people carried one way, the other half the other way. Then there was a poll and it came out something like 80% tip up.
The first clipped knives produced many years ago seemed to all be tip down, then Spyderco started making their knives with molded FRN handles and they had to be tip up to work. The popularity of these models seemed to sway most people to tip up.
If you carry a waved knife it has to be tip up to function. Or if you use a lanyard it has to be carried tip up to be useful.
People argue that it is safer to carry tip up. I have read as many or more people that sliced things carrying tip up as carrying tip down. Your knife can move around in your pocket and the seam of the pocket won't protect you anymore. If a person is scared of their knife opening in their pocket then they need a different knife, or carry your knife in a sheath.
I've carried both ways, for a long time. Tip down is significantly faster and safer for me. Granted when I carried a tiny knife it worked about equally well both ways. When I carry a real knife (meaning long knife) it only works tip down. People continually ask for a Spyderco Military tip up, that thing would take you 5 minutes to open.
I searched youtube one time for how to open knives carried tip up. Most of the videos seemed to use slight of hand to prove that tip up worked. The only person I found that seemed to operate the knife normally and make it work tip up was wearing pajamas in the video. I never wear pajamas, even at home, so this didn't apply to me. I wear jeans that are usually pretty tight and nothing goes into my pocket past the knife except the tip of my thumb. All I can grab of the knife is the end that is sticking out. So it seems to me that to make a tip up knife work you need a tiny knife carried in pajamas.
And of course YMMV.
Basically the simplest way to remove a folder from your pocket and open it.
It's already in the correct orientation to be opened without turning it around...
It's not about speed for me, more about the natural way that a knife should function when being removed from your pocket.
My knives seem to be split evenly between tip up and tip down. Tip up is totally backwards for me. When I pull the knife out it is in the wrong direction for opening, I have to toss it up in the air and catch it after it has rotated a half turn, then I can open it. When I pull a tip down knife out it is in the correct orientation, with the tip of my thumb right on the thumbstud or thumb hole. I tried putting a Military in my pocket and held it where it would be if it was tip up and then I pulled it out. The tip of my thumb was 3" from the thumb hole. No easy way to open the knife from there. I had my daughter take step by step photos of my drawing both ways so I could post them in these threads and I never did, now I have to try to find them.