Life Insurance Networking.

I understood your point that when meeting with people (networking) I should only make rapport with them (Make friends). and not sell them life insurance or ask them fact finding, probing questions (prospecting). I would like to know how should I offer my life insurance services and product so that they will agree to meet me in near future.

Building rapport isn't the same as making friends.

If asking questions isn't allowed then don't agree with that idea. Networking is a two way street... you want the other person know what you do and who your ideal client is too.

Who told you this? When you meet new people it's natural to ask and talk about what each of you do for a living. Develop an excellent "elevator speech" or something along those lines work it from there.

I'm in Life Insurance sales as well.
I find that I am networking almost every situation these days.

IE. Shopping in Wal-mart
I come across one of my clients in the dairy section, she has a child in her cart that I don't recognize, so I ask. Turns out this is her niece, and she introduces me to her little sister (now living with her) as her "life insurance lady" to which the little sister replies "OH, I have been meaning to look into that."
The big sister refers me by saying I would be able to work within her budget, I ask for a phone number and hand her my card.
"I'll give you a call next week. Does that work for you?"
"Sure!"

IE. Attending a Tupperware Party
One of my clients at the party asks a question about her mortgage insurance, then introduces me to a friend who is buying a house this year. I find out where she lives, then ask her if it's alright that I get her phone number from her other friend after Christmas, and she says, "that's great, thank you!"

These are two examples. Since I have developed rapport with existing clients, and their introductions of me to their friends are positive, it becomes easier to ask a few questions and then make a suggestion to call them at a later date.