Facilitating Microscope can be hard because no-one is allowed to say “no” to a player during their turn but you still have to teach the limits that the game does need to enforce during a player's turn. The trick is to teach by example when you can (that's why the advice is to always take the first turn), and to pause the game for “teaching moments” without actually saying “no” so you can prompt the player to review the relevant rule and get some guidance on what the game needs at that moment.
Avoid vetoing — prompt them to think differently instead
For the specific example of making an Event-sounding Period, instead of “no”, prompt the player to just think bigger. They can have their Asteroid and Period too.
Say something like “A Period needs to be able to have many, many events in it. Think ‘the Civil War’ rather than ‘The Battle of Fort Sumter’. You can still say the Battle was the start of the War Period in its details.” Then ask them to think about what the larger Period around that asteroid impact would be, and make the Period about that. They can even still say (in the details) that a big asteroid impact defines the Period. (Later, that impact can be an Event itself to explore further!)
For an asteroid impact, this is actually pretty easy, because you just have to think about the surrounding circumstances and/or the fallout — like you did. You just have to make it a suggestion instead of a “no”. For example, either of these would be fine as Periods, and the player still gets to say an asteroid smacked into the planet:
The Long Winter
A major asteroid impact plunges the planet into “Nuclear Winter”
A period of bombardment of small and large asteroidal bodies changes life on [planet] forever.
There are lots of other variations that would be fine too. Ideally, let the player come up with the larger Period's idea rather than throwing suggestions at them. Evaluating your suggestions soaks up their attention, which can actually make it harder for them to sit back and come up with the Period. (Recall the game's advice here that it's OK and desireable to give the player whose turn it is quiet, mental space to come up with their turn's History addition.)
Facilitating Microscope always comes with a lot of tension, because as a fellow player you don't have the authority to say “no”, but as the facilitator you're trying to teach what the game is requiring of the players during their turn. So in general try to avoid saying “no”, and try to offer a vision of what would be more awesome, and then explain how that's more like what the game is asking them to do.
A side problem: Avoiding sounding like “the GM”
One knock-on problem I find is the need to avoid giving the impression that the players need my permission during their turn; this is intensified by the fact that they're used to me being the GM in more traditional RPGs we play. To combat that, while also attempting to facilitate and guide the players into Microscope's rules, is to emphasise repeatedly that they have ultimate autonomy during their turn, so long as they don't contradict the established History. Laying this foundation makes it easier to avoid that impression when I have to correct someone on the rules during their turn. It also makes its easier for me to think in terms of soft guidance, rather than “no” or vetoing, in the way that I phrase any game-pausing explanations I end up making during a player's turn.
If all fails, it's OK to let a too-small Period happen
And, in the end, it's not that bad for the game if one Period ends up being a bit too much like an Event. The problem that causes may not even come up, if it's not “big enough” to attract other players' attention and attempts to create within it. And if people do build within it, the cramped nature of an Event-like Period will become more obvious, and a teachable moment.
This fact that it's not a huge problem to allow the cramped Period gives you more leeway to let it slide if your advice is too soft to fix it, or if the player insists on making it anyway. You can advise, and just let it happen if the advice doesn't stick. You can always come back to it after the game, since everyone will understand the issue better after having played the game through once.