I once saw a manager attend a phone call even as she met and spoke to us in-person. I was impressed by her ability to seamlessly juggle between the two conversations. But later it occurred to me that by doing both these things together, neither of them was important enough to deserve her full attention.
The problem with multitasking is that you are always busy. When one activity has a lull for a few seconds, you switch to the other one. Your mind is always occupied. On the other hand, by doing just one thing, you are bored if it does not engage you. This boredom indicates how relevant that task is for you. If a meeting bores you to the bone, you have good reason to turn down a similar invite in the future.
Multitasking seems impressive on the surface. But beneath the surface, it indicates an inability to prioritize.