First of all, you should (almost) never be entering start and finish dates
for tasks at all. Project is not designed to document a schedule you have
already come up with independently, it's designed to take information on
what tasks need to be done, your estimate of how long each task will take,
the relationships between the tasks, and resource information and from that
calculate the individual task start and end dates for you. You don't tell
it the schedule you want to work - it tells you the schedule you'll be able
to work.
Imagine we're building a shed and can start on Monday. It'll take three
days to lay the foundation, 5 days to erect the frame, and 4 days to put on
the roof. We have to have the foundation completed before we can erect the
walls and we have to have the walls in place before we can put on the roof.
Foundation is a predecessor of walls, walls are a successor of foundation.
Likewise at the same time walls are also a predecessor of roof. If we start
the foundation on Monday the earliest walls can start is Thursday, the day
after foundation finishes. Project's reason to exist is to calculate that
for you - that's why adding the predecessor caused your dates to change -
they HAD to because it's physically impossible for the task to start until
the predecessor allows it to.
HTH