The bad news is that affairs of any kind with old flames from our youth are the most dangerous kind and present the most significant threat to an existing relationship. If a person leaves his/her marriage for the old flame, unlike most relationships that start from infidelity, these relationships have a much better survival rate. Shirley Glass in her book Not Just Friends mentioned the research that backs this up and endorsed it from her 25 years of therapeutic practice.
I also tell you this not to frighten you, but to validate your feelings that this is certainly not as trivial as your H is making out. It is in fact, hugely threatening and serious.
The reason these affairs are so dangerous is because the old flame comes to represent lost youth and a time when responsibilities were fewer, when they were both more physically beautiful and when every day seemed like a wonderful opportunity, when anything seemed possible. All those feelings get mixed up and invested in the old flame, irrespective of their current lives and how they look/behave now.
Your H needs to understand all this and realise the trap he has fallen into. He also needs to work out why this happened and what it means. Why he had these yearnings now. It however doesn't mean that he was dissatisfied with your marriage or you at all. It might mean that he is dissatisfied with other aspects of life and therefore his yearning is for those things to change, or if that's not immediately possible, to escape for a short time.
If these communications were restricted to online activity or texts, your H might have perhaps under-estimated the danger, deluding himself that since he wasn't having sex and didn't intend to, this was just a bit of escapist fun.
But he needs to come out of that reverie and stop minimising both the danger of his actions and the impact it has had on you. He also needs to reverse this situation and imagine how he would feel if you had been doing this - that is true empathy.
You might be buckling under the pressure to stop feeling as bad as you do and even telling yourself that this is no big deal, he didn't have sex.
But what you're feeling is healthy and normal. In fact, you have a much better grip on this than your H. You know absolutely what the risk was and you are feeling this way because your safety and security has been threatened.
It might help to show your H this thread - and also buy Not Just Friends, because it explains this in great detail, with several references to online friendships and the secondary addiction to the instant fix the technology provides; the excitement when a message arrived in the inbox or when the text alert pinged.