Got an internal offer, but more to think about

The opportunity appears to be good. it is new, exploratory and I like the whole team there. The leader has very good vision and good reputation. The only thing I want from them is a higher title, which really is important to me if I want to jump to other company. The HM does not seem to give in to that request. So I told her that I like the job and the opportunity but will think it through.

I let my own boss know about this and that I am seriously considering this offer. He urges me to consider it carefully. Frankly, if it were not for my boss, I would not have any hesitation to take the offer. Boss treated me very well. we have built up a good relationship that I hate to see myslef destroying now. I am very grateful to him and feel extremely bad that I may choose to leave at the moment he needs me most.