I'm guessing that the response from a skeptic would be that brain activity can be monitored and measured over time, studying effects of different stimuli to induce said feelings and see what the results are. Therefore, because it can be measured, studied, and quantified it means it is a real thing. This is the nutshell answer, I'm sure there will be more to follow as others post their comments :)
Thanks Thparky, you're right, that's exactly what my friend said. But my response was, but you're measuring effects of feelings, you can't put anger or love into a glass, you can't hold feelings in your hand or see them with your eye but they're still real. How about wind? You can only measure its effects and feel its presence, I'm not sure it can be touched per say. I daresay maybe God is similar, you can see the effects of a higher power (like creation) some can feel His presence but you will never be able to touch God and use a measuring tape on Him to prove He exists. Doesn't mean He's not real. :)
I'm afraid I'm going to be that person who tells you that how you feel or perceive also doesn't mean God IS real. I find it more inspiring to think of nature as a vast machine that produces endless beauty and ugliness, and often both at once. What it took to get from a single celled organism to you or me is a grand story that can't be written or imagined, but that doesn't mean it isn't real either. All the small things went just right to get us here, and we're only beginning to learn how.
I could say the same thing, but it's not yet possible to determine the outcome of any brain activity (if we're still talking about feelings,) in any way. Maybe you could determine joy or love by examining the dopamine or seratonin release in the brain.
But feelings is part of the meme. We give alot of credibility to something that we haven't experienced ourselves such as believing a person if they identify as another gender simply on the fact they feel like it.