Addiction can be parsed down into multiple sub categories - physiological addiction (which is what happens with anti-depressants) occurs with virtually every drug that you use over a prolonged duration.
Dopamine based addiction (a subset of physiological addiction) is centered around addictive behaviors (i.e. consumption of opiates) that stimulate the "reward" center of the brain and offer immediate feedback.
When people think of getting "addicted to a drug", they are normally referring to the latter. Anti-depressants are commonly used as part of treatment programs to help people overcome substance abuse issues or destructive compulsions like gambling.
But, I suppose at a very high level, you are right, anti-depressants are "addictive" in the sense you can't just drop it cold turkey without some horrible side effects.
Regarding the latter question, the statement is not baseless, but it's framing the issue in a really deceptive way. Has the use of anti-depressants contributed to acts of violence or self harm ? Yes, but in an extremely small number of cases. Have anti-depressants mitigated against acts of violence or self harm? Yes, by orders of magnitude more than any harm they potentially cause. Anti-depressants have efficacy scores that exceed 95% for people who have attempted suicide, but later sought medical intervention.
Don't get me wrong, I personally feel that anti-depressants are overprescribed, particularly to young people. They also don't work for everyone, and some people may need to try multiple therapies before they feel better. However, on aggregate, they play an instrumental role for people who suffer from not only depressive disorders, but anxiety, OCD etc.
It's important that we don't paint in broad brushes - it is a nuanced problem, and statements like "they are addictive and cause violence" aren't helpful.
