The Ministry warns against meddling with time because the common consensus is that through time one can unmake the world, erase one’s forefathers from existence, or trap all living beings in a complex loop of start and go and back to start again.
But time is a great deal stronger than that. One may go back a few hours, weeks, years, or even centuries; and there will almost always be a powerful force that checks the meddling, that keeps the world from descending into chaos. So you want to visit your ancestors? Very good. It will likely turn out to be necessary: great-great grandmama and darling great-great grandpapa will never meet, unless you should take it into your head to make the introductions.
No, meddling with time is banned because there is one terrible thing it accomplishes, one kind of glitch that recurs, over and over again, when human will triumphs over time. When wizards and witches first began to experiment with time, it was not simply to greet their forebears. It was often because of a niggling thought, persistent and overwhelming: I wish I had never been born.
Time, for some reason, will make accommodations for that sometimes. When the person is alone. When the person is young, full of wild thoughts, undisciplined. When the person has not yet made their own special mark on the universe. And so it is not to save the world that time magic is highly regulated. It is because of the lost potential. It is because of the suicides.