Time moves forward, not backward. Causality dictates that cause comes before effect, beginning before end. So, to have an eternity of past makes no sense. You would have an infinite number of causes, which were in turn effects of previous causes. This leaves you with a causeless reality, a series of effects without cause. Dominoes falling with no first domino.
The illusion of it making sense derives from looking at time backwards.
You are here at P. Looking ahead, it makes sense that time continues forever, no ending point, just effects causing more effects, and more, and more, continuous. No problem here, causality has nothing against effects becoming causes for more effects endlessly.
Here's where the illusion starts: looking backwards it may seem to make sense that time had always existed forever before hand. You can think back 3 billion years and just keep subtracting millions and millions, and even billions endlessly, because you are looking outward at it.
It's mathematically possible to keep subtracting centuries and centuries, but realistically impossible due to causality.
Because time moves forward, you must apply that to your vision of the timeline of existence if you want to test the accuracy of this notion that time had no beginning. But you can't. There is no starting point, you have nowhere to beginning the forward view of time. Jumping to some random point of time doesn't count because it just takes you to looking at the infinite history backwards again, drawing the same illusion.
A great noteworthy example: Imagine a boy who had never been born, who had always existed. Because you live from birth to death, and not the other way around, he'd have to have experienced an eternity of life already, but that doesn't make sense. How did he get to this point of his life if he had to live an endless amount of time to get there, considering eternity has no end? How could he have an end with no beginning? How could he exist if he never entered existence?