“If I give birth to my child in, for example, Canada, then the child will become an automatic Canadian citizen. Will I also become a citizen then?”
While your Canadian-born child will automatically acquire Canadian citizenship at birth, that will do nothing for you.
You are still ‘only’ a citizen of the country that issued your passport – or also a citizen of a second country, if you already were when you entered Canada. But giving birth to a citizen of Canada will not give you anything – except, of course, a great baby.
ADDED: Having a Canadian citizen child might also get you the right to immigrate in the very distant future, once the child is old enough and qualifies otherwise to petition for you. But that gets you nothing otherwise, until that time.