It's unclear how this person was "laughing" in your description. Did they write "ha ha" in the email or use emoticons or something? Did you hear them laugh about it is some other context? My experience is that a lot of people cannot handle critical feedback about their work and interpret it as a personal affront. One of the big problems with email (and other written communication, such as this one) is they lack the visual and auditory cues that add a lot of context to a message. Our imagination will often fill in those gaps for us without us realizing it.
If you are basing all of this on an email conversation, you should probably take a deep breath and reassess the entire situation. Consider that if this person is giving honest critical feedback, responding in the way you did is extremely unprofessional. If this person carries clout in the organization, this could have some severe negative repercussions for you in that organization.
I once had a subordinate who would regularly accuse other people of being unprofessional and 'attacking him'. It became clear that this was all in his head and really these were completely normal and acceptable critiques, advice, and clarifications. Once this was realized, he was let go with very little ceremony as he was being disruptive and creating a hostile environment for his co-workers.
You might want to read this post and consider if you might be perceived in the highly negative way the subject is viewed.
If you really want to get on top of this, you should meet with the person face-to-face or on on a phone call if that is not possible. The subject of the conversation should be "I understand you have some concerns about my presentation. I would like to discuss your concerns and how you think I could address them." If the person is sincere, then you can listen and determine whether you agree. Perhaps even if you don't you can make a concession or two in order to placate this person. If this person is really trying to insult you, this will allow you to firmly assert that you are not intimidated and in control of the situation. At no point should you engage in an argument. Listen to the what he or she has to say, get any clarification you need and say something like "thank you, I will take your feedback into consideration".
At the end of the day, whether or not you like this person, it's better to have them as a friend or at least a neutral relationship than to have an enemy. There's really no upside to being hostile to people in your organization. If this person is a jerk and you take the high-road, people will look at the other person and say "what's his/her problem?" If you get dragged into a fight or a war, then they will see you as part of the problem.