There are several fundamental problems:

• the huge distances
• the enormous fuel requirements
• human concerns

Distances:

The closest stars are 100 million times the distance from the Earth to the Moon.

Travel times will be much too long (in human terms) unless spacecraft can attain speeds close to the speed of light (the limit; faster than light travel poses time travel problems).

The fastest spacecraft built so far are still much too slow ( Voyagers will take 80,000 years to reach the nearest stars).