How did Voyager (the ship) get it's bad reputation?

Not to mention, think of all the Delta folk passing copies of the Cynics Corner reviews on to their neighbors.

 

It dumped its garbage frequently into space. This caused spacial warning that resulted in the deaths of millions. This is why it was despised by all who encountered it.

 

And warp plasma, don't forget that.

 

Voyager created numerous plotholes where ever it went, endangering the fabric of space itself.

 

Have you watched the show? Voyager was PULLED into the Delta quadrant by the Caretaker. Also, they weren't the only spaceship out there traveling from planet to planet. No, the Kazon wanted to capture the ship and use it's technology so spreading lies about Voyager was a ruse to keep them from forming alliances making them easier to capture.