The past cannot be changed
COLE: (moving his head to see the film) I have seen it, but I
don't remember this part. Funny, it's like what's happening to
us, like the past. The movie never changes -- it can't change --
but everytime you see it, it seems to be different because you're
different -- you notice different things.
This movie is an example of self-consistent time travel: anything you do has already happened, including the results of your time travel.
Your actions can have an effect on the past, but that effect has already been seen in your present.
For example, Cole tries to stop Dr. Peters from taking the virus on the plane, but has to fail, because the virus already exists in his present.
ANGLE ON YOUNG COLE, as his FATHER'S ARM drapes over his shoulder,
steering him. YOUNG COLE turns to look back as he's led away.
YOUNG COLE'S POV: the PARAMEDICS, exchanging glances, shrugging
helplessly. It's too late. The BLONDE MAN is dead.
As such, he can take actions that are consistent with the future, but not ones that are inconsistent, and any consistent actions he takes are predetermined.
As @Hypnosifl says, it seems that James Cole may not have given Peters the idea to release the virus.
DR. PETERS: I think, Dr. Railly, you have given your alarmists a
bad name. Surely there is very real and very convincing data that
the planet cannot survive the excesses of the human race:
proliferation of atomic devices, uncontrolled breeding habits, the
rape of the environment, the pollution of land, sea, and air. In
this context, isn't it obvious that "Chicken Little" represents
the sane vision and that Homo Sapiens' motto, "Let's go shopping!"
is the cry of the true lunatic?
However, even if he did, it would be consistent with Cole's present, and thus allowed.