No it won't. Not unless it has an insanely long life span but I'm not convinced it will.

Put it this way the DS didn't outsell the PS2 and the Switch is behind the DS in the charts.

I made my prediction slightly bolder than I have it in my mind and said yes. At the moment I'm thinking the Switch will fall slightly behind the Ps2, cause looking at Vg Chartz numbers the Switch will easily outsell the Ps2 in Japan+rest of world combined, but I think it will fall behind in the Americas+Europe enough to fall 5-10mil behind. This could easily change if we have huge numbers after March 3rd next year.

Depends on how long it is on the market, and how a mid gen refresh is handled. But even then...it will be hard. The PS2 enjoyed a 10 year lifespan with the lions share of 3rd party support. Even after its time, it also had its price cut to $99 at retails for a time. This made it the ultimate budget console. The PS2 had a lot more going for it based on the timing of DVD players getting big too.

It is not impossible, but a number of unique factors outside of already impressive library on the PS2 side will make it very difficult.

Yes, it will.

105 million by 31 December 2021
130 millions by 31 December 2022
147 million by 31 December 2023
159 millions by 31 December 2024

There's going to be a Mario kart 9 on Switch and Pokémon Legends will sell Unit's also I think there are more 3rd party exclusive Unit sellers still to come. For example, Shin Megami Tensei V will sell Units in Japan and rest of world. So I don't fully agree with your software point.

The Ds was a faster seller than the Ps2.

Yes, and no.

We didn't get another 3D Mario (neither the Super Mario 3D All Stars collection nor 3D World and Bowser's Fury is "another 3D Mario") so there is still room for this to happen. And we al know what "3D Mario" means, it means 10+ million sales, 97 on Metacritic, an redefining what a great game it is. We didn't get this since Super Mario Odyssey, and I am still hoping for Odyssey 2, just like Super Mario Galaxy 2 was way superior to Galaxy 1.

And we'll get an open world Pokémon game, which is requested by the fans for ages.

And Splatoon 3 was anounced 2 months ago, so I don't understand your point about Splatoon 2.

And regarding Zelda games, we have a second one coming, aslo anounced.

And Metroid Prime 4 of course, and Bayonetta 3.

And I still believe Mario Kart 9 will happen. Not now, since the sales momentum is tremendous, but at some point.

Absolutely. It has the tools, the time and the popularity to do it.

Nintendo's shipment number was 79.87 million as of December 31st 2020.
If the Switch sells this year similar to last year, 28 million units, and has a heavy drop of like the Wii, a cliff if you like it would look like this at the end of each year:
2020 - 79.87M
2021 - 107.87M (28M)
2022 - 130.87M (23M)
2023 - 148.87M (18M)
2024 - 161.87M (13M)
2025 - 169.87M (8M) Successor launch here
2026 - 172.87M (3M)

The Wii saw a drop off of 5M per year, everyone calls that a cliff. So if the Switch also experiences a cliff starting next year it will easily sell over 170M units, way more than the DS and PS2. That would basically be a pessimistic prediction.
The earliest I see it possible for the successor to launch is 2024, not only because of Splatoon 3 and third party support only now starting to ramp up, but also because Furukawa pretty clearly said last year that we were in the middle of the Switch's life and it would have a longer life. That's why I see 7 years as the shortest it will be.

Edit: There also hasn't been a pricecut thus far. I don't think any console ever sold 80M units without ever getting a pricecut.

Well, it seems quite inevitable that Switch will outsell PS4 (which seems to stop at about 120M). But PS2 is a tall hurdle to clear. So not sure.

Currently I would put the chance of Switch outselling PS2 at about 30%. That is a realistical chance, not too unlikely. Remember, that is about the chance 358 gave Trump to win against Clinton in 2016 (2020 against Biden they put that chance more at 10%).

There are some major junctions, that may influence this probability and that totally depends on Nintendo and their plans. These are: new model, price cut, Wii sports like game (or even evolution like Ring Fit Adventure over Wii Fit) and the release of the next console and how fast Nintendo will drop Switch support in favor of the next console. If these things happen in favor of Switch it could well be selling past PS2, if they happen unfavorable the Switch sales could stop just above 120M.