Why Can't Anything Travel Faster than Light?

[Rhondazvous]

Doesn't that create a paradox or at least an infinite loop? If time stands still at c then v = 0. which means m is not traveling at c so time doesn't stand still meaning that m is traveling at c where time stands still and v = 0, ad infinitum.

So, yes in a sense taking the limit of v=c as an observer is not a mathematically consistent thing to do and you encounter things like 0*infinity that by themselves aren't meaningful. But you also have to be careful how you define the velocity v - the velocity of photons being c is measured in the time frame of the observer, not of the photon.
Every object is at rest from its own perspective, and to square that with lightspeed always being c leads to the extreme ( and not quite mathematically consistent ) limiting case of time stopping. Then from the photons perspective, it doesn't move but also no time passes, so the speed is 0/0. This tells you that the vantage point of the photon isn't really a mathematically valid reference frame.

"Every object is at rest from its own perspective"
Except the brain of a field theorist which can single-handedly keep the Tylenol industry in business for several decades.

If no time passes, how can light have a speed? It would already be whereever it's going. The very idea of going somewhere implies a time