Switch is supposed to launch in March, if this rumor is true, then Breath of the Wild comes in somwhere between May to July. 2-4 months, big freaking deal. As far as I know, there's no other big title planned to launch in Summer, so chances are, whether it's releasing in March or Summer, it'll be the #1 big title everyone buys or plans to buy with the only competition being Horizon: Zero Dawn, and that's BEFORE it's first holiday season

It needs to launch at or around launch to reach those numbers, I'll give you that one. If it's not at launch, 2-4 months is still around launch, which will still have it in it's favor because that means the game will have the Switch's entire life cycle to reach the mark.
Besides Twilight Princess (7.3 million Wii alone, 8.9 total), Zelda 1 (6.5), and A Link to the Past (4.6) no other console Zelda game has ever been released within the first year of its system's life cycle.
So if Breath of the Wild releases right on the day Switch comes out or 3-4 months after, history show that it's still in it's favor.
Part of it also has to do with what the Swtich will have and how it's momentum will be carried AFTER Breath of the Wild is released. BotW and 3D Mario, right out the gate gives it a great start. 

But this is assuming that the rumor is true and BotW is delayed a few more months, and I still say, if a 3D Mario is ready to go, that's the launch title, otherwise, Switch will be delayed along with it. 

You are just making assumptions. Just like the game could be released in May, it could be until Nov 2017 or even pushed for a later date.

And if that happens, what are the chances from Nintendo releasing a game on a failed console that ended production a year befor and has been 100% replaced for almost a year?

There's no way it's getting pushed back to 2018, I can tell you that now.
The game is close to finished. Why on Earth would they feel the need to push the game even further back than they have to, ESPECIALLY when it is such a crucial, heavily anticipated title that they need for the launch window of their new system.

Edit: Got my years mixed up. Oops.

And it will be even better to have it launch. It will help the Switch to sell faster than a 3D Mario (initially, because Zelda is not an evergreen title like Mario).

If they are just pushing to May, it's ok. Holiday? Terrible. But I want to believe it is going to be at launch and my hope will remain until January 12th.

That's all we can do in the meantime. Wait 2. More. Agonizing. Months.

You criticize things they've done in the past, but I have never, ever seen you say anything critical about their current or future plans, and not just now regarding Switch, but in the entire time you've been on this forum. You are free to prove me wrong, but I think you would defend absolutely anything Nintendo did, until it was in the past.

Nintendo's rampant, out-of-control delays are a worse habit than games releasing slightly imperfect and being swiftly updated. At least other companies get their games out in a reasonable timeframe.

Except the games released today are more than slightly imperfect the experience is damage to hell in a number of cases ask console players of Skyrim SE how they feel about the past week and a half when Bethesda's patch caused the game to crash when loading the game on all platforms rendering it unplayable, PC players had to patch the game themselves. Many of them are literally saying would take a delay to not experience forking out money to go through that as they're livid especially after the debacle of the original Skyrim release and Fallout 4's problems that it's began to hurt their rep with their player base and fans you can even go to Bethesda's support forums to see examples of what I mean.

Sorry but anyone advocating such practice needs to sit down and think because it's horrid to go through, Dishonoured 2 PC players are going through it now and this is after having a day 1 patch as well. The majority of people would rather have a polished game in their hands than go through that and Nintendo wouldn't want to have to continue working on and patching the game after it's released as it impacts resources for future projects.

Sorry but delays are better than that nonsense, it's not even a debate at all.

Yep, I actually prefer delays to unfinished, messy, broken games. Still, it's Nintendo's fault to set a launch date and delay it. I think that's common in gaming industry nowadays, and it's very irresponsible. It's best to keep giving updates on how the gane is going wirhour a proper release window, and just state the date when they're 100% sure they can make it. Even if it's 2-3 months before launch.