The problem with that is simple math. Well it actually isn't simple, as the equation is quite long - but it produces a simple, yet overwhelming, problem.
The amount of energy it takes to propel a space ship the size of a small car, with just one person on board in hibernation. No food, no water. Just a ship large enough to carry one human and an enclosure.
The amount of energy needed to travel just one light year is unthinkably large. Roughly, about 7 x 10^{17} joules. Or about 52 million metric tons of modern rocket fuel. But that is just the beginning. Now you have to propel 52 million tons of fuel too! And now we are talking numbers that get mind boggling. And it just keeps getting worse.
"Oh! - but we will discover a super cool energy source that has infinite power!!!" - like Star trek!!!
Yeah - well that doesn't work either. Something called physics. A super neat fuel source like that would create unimaginable problems. How on earth would you contain it? How would you manage to control such power and be able to throttle it? A fuel source that roughly has the power of a small star that only weighs a few hundred pounds or something?? What could it possibly be made of? And how would you obtain such power without, literally, blowing up your own solar system. Like - literally blow it up.
And on and on and on.