Welcome to the forum. It's great you have found your way here and want a conversation on self hatred. Sadly it's true that many people feel they are not good enough for the world and dislike the person they are. You are right that letting people help you is a good start to getting rid of these dreadful feelings.
Not knowing who else is in the group I cannot make specific suggestions. I wonder if any of the group members have been in this sort of group situation before and have become used to sharing their stories. I also know that every one of us sees our own circumstances differently. This is one of the strengths of posting on this forum and of talking in a group setting. Well done for trying to join in. We see ways of coping that we may not have thought of on our own.
I'm not entirely sure you must love yourself before loving others. I know this is something I took for granted but over the years I am less convinced. If you put energy into helping someone you often feel good about it and that is a good feeling. May I suggest you think about what or how you can do something for someone(s) in your group and focus on that. It does make discussion easier for you and can help you make some disclosures about yourself after a while.
When we focus on our own self dislike it is hard to chat because we are usually ashamed of being such a bad person. It's not true of course but it is a huge handicap. So focus on the others and talk about what they are discussing. It helps you to feel included and the others to feel you care and are interested in them. Talking about yourself will become easier as you go along. Listen carefully to know what the others are saying about themselves and see how much you share the same or similar experiences.
When I started posting on BB I was frankly scared someone would know who I was (did not happen) or that I would show myself up as an unpleasant person(no again). I have been in groups similar to yours and yes it can be daunting to join in at all. Even more so to talk about yourself. I felt I was unworthy of such attention. Does this strike any chords with you?
Please persist with your group. Maybe you can share how hard it is to open up at all. I would love to continue this conversation.