I think your analysis is not complete.

Yes the Euro is/was stable but not because there are many big countries using it.

The Euro is/was stable because behind it there was stable and relatively well managed democracy named Germany. Unfortunately Germany is not doing so well at the moment and that could deteriorate even faster in the future with the right wing populist gaining grounds who are openly campaigning on leaving the EU and the euro.

As you can imagine, without Germany, there is no euro.

The Euro also spreads the risk to other countries which means that one state's failure can propagate to others.

Look at what happened with Greece and the panic that it caused at the time and that was for a small country witha small GDP. Now look at France who is indebted to its eyeballs and on the verge of electing either a far-right or far-left president who both are EU-skeptics and will try to work around the EU if not completely undermine it.

What happens then? As always in a chain, you are only as strong as your weakest link and unfortunately for the Eurozone, France and Germany are both doing badly at the same time and it doesnt seem that there is any light at the end of the tunnel for both of them currently.

Italy is doing slightly better but its economy is smaller and it is still heavily indebted and it will not be able to carry the Euro itself if either France or Germany decide or are forced somehow to exit the Euro.