Way I figure, if you can create a stable time loop, then an unstable one must also be possible. The latter would completely fuck up everything, forever, and in an infinite universe, probability states that it would have already happened, many many times, assuming the first one didn't destroy everything for some reason.
Try it this way:
You don't create a time-loop. You are merely the bit of the universe that creates said time-loop. The entire
universe that creates the you that creates the unstable time-loop is non-valid. It's a bit like trying to justify the (hypothetical) chances that your grandma from the Titanic survived to meet the handsome midshipman on the rescue ship who was your grandfather. They did, thus you exist. Had they not, you would not have been around to ask the question. But in an even more meta-chronological basis.
Or... look at a woven tapestry, where some of the longitudinal threads loop round and displace earlier threads... Looked at from 'outside the tapestry', the loops in shove the threads around to define whatever threads need to loop out. As far as we are concerned, it's a valid tapestry if the threads aren't broken. Live
in the tapestry,
being a thread, and you experience everything 'happening' around you as the threads are woven in and out of one another and
occasionally a loop-back interfaces with you, and then some thread (you, or something/someone else's) exits to
be that loop. In a view of 'tapestry time' it's coincidental that it's self-fulfilling prophecy/action/'interference'. From the external observer, that's just the way it is. (There may be many other 'valid' tapestries out there, and the ones that aren't are never 'exhibited', for no-one to experience[1]). Leaving you with something like the questions involved in the weak-anthropic principle. The answer: you're here because things worked out. You would not have been if they had not.
(In a more mundane, non-timeloop set of examples: Grandma got picked up by a different rescue ship; Grandma did not survive the Titanic; Grandma was never
on the Titanic, in the first place; Grandma was born a boy; Grandma never existed
at all, for other historic reasons. The relationship of the electroweak force to the Planck Constant (...whatever, could be anything!) meant that matter could not condense in the first place out of the Gluon-Gluon soup (...again, whatever) and there were never any stars and planets in the first place to allow... well, it all to happen in any way that led to your existence.)
And, like I said, this is but one among many possible 'solutions'. Re-branching at each 'poke from the future' intersection of reality is another. As we don't have any idea what the 'metaverse' looks like (heck, we're still trying to get an idea of the basic tennets of the bubble that is our own Universe...) right now it's an open question.
I tend to go with it being a whole lot of bubbles. Multidimensional bubbles. The surface of each bubble represents space-time for the universe it represents (see also my "latitude is time" post, but that may not be necessary), and in the metaverse the bubbles... exist. Perhaps all the ones with fatal flaws in their structure popped, ages ago, but
not in our variety of time. I've no idea if the bubbles ever 'link up', or even form a foam. I'm already out on a limb with the basic concept of
at least one bubble being visible (from whatever viewpoint one might imagine exists
not being restricted to being just within a bubble) in the entirety of existence. I could not, in good faith tell you that even
this is 'reality'. But it would work. And it would (IMO) be elegant, which in the absence of any other cues always seems to work when it comes to these sorts of theories. Or at least better highlights when there's a fatal blemish.
[1] If you
insist, then the ones with broken-threads, or with utterly 'impossible' interactions in them might still be 'lived' by tapestry-thread-beings who find themselves regularly shoved over by temporal anomalies, see impossible interactions (where discontinuities in the structure are observed from the non-tapestry POV, disobeying the basic rules of tapestry weaving for the sake of accommodating loops, or of
denying loops that should have occurred by the particular rules of tapestry-weaving but that just
cannot be patched back into the 'prior' material, for whatever reason). But I prefer to imagine that there is 'life' only in the tapestries that have been produced by the metaverses weavers where the consistencies resolve.