OK, we are talking about speeds, and the fact that there is a limit to speed. Thus we are talking about motion. Motion contains two variables. One is speed, and the other is distance. Variables range from zero to infinity. Thus to look at the biggest picture possible concerning motion, one would naturally push both of these variables to infinity.
To travel at an infinite "speed", means to travel across any distance, in zero time. Meaning, one could travel from point A to point B in let's say 1 minute, but that also means that you could travel faster and complete the trip in less than say just 1 second. The faster you go, the less time is required. These are finite speeds. But if you travel from point A to point B in no time at all, then there is no way that you can beat this particular speed. This is the infinite speed.
Next. To travel across an infinite "distance", means that you will go on forever since there is no end to an infinite distance. Thus if you combine the two and travel across an infinite distance at an infinite speed, this means that you will go on forever, in no time at all. Holistically, this is simply not possible. However, relativistically, it is possible, and it is possible since the two extremes become separate.
In one possible extreme, you may move across space but will not be moving across time. In the other possible extreme, you will be moving across time but not across space. To make this transition possible, if you gain in one, you must lose in the other. Thus you can't have both extremes at the same time. Thus they in turn must be encompassed within a finite to cause this gain and loss phenomena.
In turn, you may be moving across space but not across time, while for those observing you, time for them is still ticking, and thus even though time is at a standstill for you, time may go on forever, elsewhere. Thus you may go on forever, in no time at all.
Thus finite motion across space-time is a requirement to make motion possible. Thus there is a finite limit to speed of motion across space.
If you then analyze the outcome of this phenomena, you independently discover Special Relativity, and independently derive all of its mathematical equations. See https://www.youtube.com/watch?v=KKAwpEetJ-Q&list=PL3zkZRUI2IyBFAowlUivFbeBh-Mq7HdoQthis video for verification.