That last sentence makes it sound like it makes you selfish and hard-hearted. I noticed it could be interpreted to be that it will make you at least one, which seems more accurate. If you desire to be kind-hearted and help others, you will either have to accept that you can't help others if you're kind-hearted, or stop trying to help others. You don't have to be selfish and you don't have to be hard-hearted, but you do have to be selfish or hard-hearted.

Also, considering Mill is considered the father of Utilitarianism, it seems unlikely that he was preaching egoism.