Being slow at times is a good thing and a freedom everybody should give themselves at times.
That being said, some people don't like being too slow. I have a collegue who is clearly too slow for health reasons (overweight/unfit). When we are walking to lunch too fast for him, his excuse sounds a lot like what you said, while clearly out of his breath, because of a lack of stamina. So he frames it as a choice where we are wrong, while he is out of breath on a medium tempo walk after 100m. When I know from personal talks with him, that he dislikes being the slow one.
The human body is built to move. A lot more than most modern people move during their typical days. Not moving it, or moving it in ways that avoid effort has serious health effects. That doesn't mean we have to move fast always, but if your reason for not moving fast is an inability to do so, that is bad both for your body and for your mental capacity.
Moving slowly can be very exhausting. Try holding out you arm in front of you for a minute. So for many this isn't about moving slowly, it is about moving lazily.
Talking about responding too fast: Yes listening is a key skill many people fail to deploy. Yet effective communication sometimes works way differently than just listening to the words someone said. Here I have to think about another friend of mine. She talks very slowly and has the habbit of talking in circles. Meaning if you won't eventually interrupt her, you will hear variations of the same thought that has been expressed in the first 10 seconds spread out over minutes. This happens even with things where the first thing she said was a yes/no question you could answer in a second. A surprising amount of people will just talk until you interrupt them. In fact they want you to interrupt them, it stresses them out if you leave them hanging to fill more time. Those people would just have to get to the point, but they seem to have an inability to do so.
Effective communication after the sender/message/receiver model happens if the receiver can quickly decode the original thought encoded into the message (=words) by the sender. Old couples for example will not have to say many words in order for the other to understand what they feel and want to express. It is like they read each others mind, because communication isn't about reading the message and interpreting the words objectively, it is about decoding the thoughts, feelings and intentions encoded in the message made in the circumstances it was made.
That can lead to complications, if person A understands person B quickly, but person B doesn't trust person A to do so. Then person B needlessly insists on elaborating until the point is reached where sufficient information has been packed into the message to get the thought across. That means person B has a mental model of how person A may understand certain words that is way to pessimistic. For bad communicators that mental model is overly broad and unpersonalized ("throw words at the other side at some point they will understand"), while good communicators can quickly form and refine their understanding of how the other side receives messages. In the best case that works like with the old couple. In the worst case someone convinced themselves they can read minds, while all they do is guess and interrupt.
That means being interrupted can mean a person thinks they understood what you were saying. If this happens often and the person opposite gets it right, that is a sign they understand you well. If it happens often and the person opposite gets you wrong, either your thoughts feel more complex to you than they are or you need to work on the way you encode the thoughts into words (e.g. lead with the least obvious thought to avoid them hooking onto the first thing).