This reasoning assumes we all have great control over our emotions. Consider the following extreme example: The death of your children can't hurt you unless you let it.
We are interconnected beings, and we have emotions. The reasoning denies these facts.
I feel like I am missing a really good rebuttal here. I am going to think about it some more.
Yes, we do have emotions. However, as humans we can control our emotions. Some people choose not to.
But we can. Personally, I know that I can partition emotions. For example, during times of significant family tragedy or problems at home, I can and have completely put it aside in order to do my job.
If it came to the death of one of my kids, I have no doubt I could do it then as well and grieve at a time I choose (i.e. I actually deal with it and let it hurt).
I'm using "I" a lot here, not out of vanity but simply as personal experience. I don't think I am special or unique. I think we all have that ability. Granted, for some it is easier than other. But that is true for almost everything we do.
In arguments, fights, and even love, if a person lets their emotions override their reason, it usually does not end well.
So yes, your assumption at the beginning is correct. However, the fact that we have emotions does not mean we have to let them control us.