The strongest argument can be put different ways, but it is really just one:
Fear of change / Never change a running system / The inability to absolutely guarantee the new system will quickly settle into a balanced and stable multi party system.
After that, what makes things complicated is that there isn't simply "the multi-party system" and "the two-party system" - once you start talking about a specific system, the arguments will get more specific and be aimed at the weak points of that specific system.
For example, first past the post's 1 rep per district system has very good local resolution - you get 1 rep, presumably living in your presumably small district, that you get to vote on. Some multi-party systems (e.g. Germany's) address this, others don't.