It sounds to me like he is perhaps just not quite ready for solids just yet. His gag reflex (which is very useful as it helps to avoid choking by ejecting objects LO is not ready for) may still be quite sensitive and in a few weeks or another month might be less sensitive. The gag reflex can result in vomiting too.
As with anything medical though it would be worth a trip to the doctor if the vomiting continues even when solids are not given.
Personally I would just stop offering for now, maybe just offer finger foods as he knows himself if he wants to eat these or taste them or if he has no interest yet. I would advise against trying to get him to eat anything, he is letting you know he is not ready by not letting the spoon go near him.
Whilst it is advised to introduced solids in a timely manner, and 6 months is the average age, it is also very much about whether LO is ready, interested, showing signs of wanting to eat and other signs such as the gag reflex not being too sensitive, ability to sit up well unsupported etc. It sounds like yours just isn't ready just yet and that is not cause for concern, he will take some food when he is a little more developed. At this age anyway even when LOs are interested in pureed foods the portion sizes are around 2 tea spoons (per meal, and 1 meal per day at 6 months increasing to 3 meals around 8 months) which is very little.
Just like crawling or walking these developmental phases come at different times for different babies. My DS was like your first LO and very interested in solid food from the off but I have known LOs show almost no interest and eat very very little in the way of solids until closer to 9 months and they have still grown and developed wonderfully.
I hope this helps ease your worry but, as I said, do seek medical advice if you feel concerned or if the vomiting continues.