So many factors here, but it certainly has a shot. But without knowing what Nintendo's plans are for a new console and the timing of it are the big questions here.
Also, if they released a Switch Pro which was just an upgraded Switch and not a new system that would certainly help to drive up sales (and to cause many people to double dip for the better system who already owned a previous version).

I will go ahead and guess that it will beat it, since I have to guess something :)

From now on, major 3rd party franchises won't come on switch. I still believe that the biggest 3rd party support that the switch will ever see is Monster Hunter and it's already done, and let's face it, 3rd parties had 4 years to make the move on the switch, yet, they kept waiting for next gen. And now they'll effectively make the transition and develop for PS5 and XSX. However, first party support might be something interesting since much is left to do for Nintendo.
For almost 2 years or more, all what nintendo's studios have been doing are ports and HD remasters. Switch is starving for first party support and objectively, it still looks like the worst first party catalogue ever for a Nintendo console.

How is that objective? Imo it's one of the best first party catalogue on any Nintendo console.

I wouldn't go that far. 1st party games are the selling point of the Switch, and it has had most of its heavy hitters by now. Many of them are considered some of the best examples of their respective series, so saying it's the worst first party catalogue for a Nintendo console is pushing it. Nintendo's been taking advantage of the fact that they have an entirely library of games that, because of the WiiU's failure, practically noone played, available for porting to the Switch. That has been great to fill holes in their release schedule. They still have some big ports left (I can't think of anything other than Xenoblade X or Fatal Frame left to port), but once that's over their software output is going to slow down somewhat.

Don't say "objectively" when you don't know what it means. You say "for almost 2 years or more". Let's see what Nintendo's studios have released for 2 years or more (so let's go back until April 2019):

- Super Mario Maker 2

- Fire Emblem Three Houses

- Luigi's Mansion 3

- Pokémon Sword & Shield

- Ring Fit Adventures

- Animal Crossing New Horizons

- Clubhouse Games: 51 Worldwide Games

- Paper Mario: Origami King

- The Legend of Zelda: Age of Calamity

- Bowser's Fury

I don't think this can be called "starving".

I doubt 3rd party support will dry up especially if the big refresh rumors are true. We know of at least 1 Resident evil game coming from the Capcom leak. So the Switch will at the very least get 3rd party games specifically made for it.

Only way Switch beats PS2 is if it gets the same boosts that PS2 received:

- Switch successor will have to bomb out of the gate like PS3 did, which greatly helped the PS2 legs.
- Switch would have to lower their price to sell at a loss. PS2 was sold at a loss for a while, with some estimates in 2001 saying it was losing anywhere between $100-180 per hardware sale. That boosted sales incredibly by having such a cheap price point. And that's not even taking the price reduction into consideration, which also helped a ton.
- Switch continues to be manufactured like crazy at least 2 years after its successor comes out.

If the playing field was fair and the PS2 was sold at break even (or profit, like Nintendo does), if the PS3 never bombed out of the gate, and if Sony greatly reduced production and distribution of the PS2 after the PS3 came out (kind of like they are doing with the PS4 now that the PS5 is out), then we wouldn't even be having this conversation as the Switch would have already passed the PS2 lifetime.

Well yeah I'm assuming the rumors are correct and that it'll use DLSS to do 4k docked. But that doesn't mean Nintendo is going to go with this strategy that I laid out. I doubt that is the plan, as it'd also split the library and stuff and it'd be confusing, but I'm just saying if they did pursue that and some how found a way to make it successful that's the only thing I could see leading to an extending of the Switch lifecycle well beyond 2024 and allowing it to beat PS2 numbers. I'm guessing it'll just be a standard upgrade that Nintendo always puts out and it won't change their whole strategy for the Switch. The upgraded Switch would probably need to be like $400 to have the power boost needed to create a "Switch 1.5" type device that can more readily graphically handle PS4/XB1 level games.

Yes, Switch will be the best selling gaming hardware of all time. It has created a new market that many didn't realize they wanted or needed. Almost everyone I know that owns a Switch Lite owns a regular Switch so they can still participate in this new market. The ability to take a home console experience with you when you travel cannot be matched by anyone else yet. I mean, are we forgetting that the Switch just had an amazing February?

“Nintendo Switch was the best-selling hardware platform in both units and dollars in February,” said Piscatella. “Unit and dollar sales of Nintendo Switch hardware in February were the highest for any hardware platform in a February month since the Nintendo Wii in February 2009.”

The momentum for the Switch is going up, not down, so this FY it will see an increase in sales, next FY will likely see sales similar to last years. Let's not forget that any variant that comes out will be purchased by people that already have a Switch. The Switch is the ultimate collectible item with custom docks, skins, joy-cons, retail box, etc. After four years the Switch will likely be in 7th or 8th place in all time sales already, and this is without a price cut.

2021 FY sells 28m
2022 FY sells 23m
2023 FY sells 18m
2024 FY sells 13m

The next four years looking like this would put it at roughly 160m units...

I think the better question going forward should be what could cause the Switch to fail at being the best selling hardware of all time.

I think the odds are looking very favorable for the Switch right now, but it depends entirely on Nintendo's future plans. If they end up replacing it in the first half of 2023 then it will probably have the same fate as the DS and fall short of the top spot despite having incredible momentum. I wouldn't really expect them to do that though, especially if they really do release a mid-gen upgrade this fall which many signs seems to point to.