The girls try to force you to go out because they like you and they would like to get to know you more in a different setting from where they normally get to see you. Going out is great but only with the right company and people that you are comfortable with. It is commendable that you don?t drink and this shows that you are responsible so do not let the girls make you do something that you are not comfortable with.
If it was me I'd go with them anyway, even if you don't drink. They must want you to go for a reason so let them do the drinking and then bring em back to your place and mix them up some drinks and you might be really glad you did ;)