It's a common thing that hearing that you've hurt your partner's feelings can be quite painful. However, that does not mean that it's now time for you to tell your partner off for hurting YOUR feelings by telling them you've hurt THEIR feelings. That's bullshit. Your partner has to be able to tell you that something you've done (hopefully unintentionally) has caused hurt. You should not shut them down for telling it to you, even if they are blunt in telling you. You hurt their feelings, and they are probably struggling emotionally because of it. Deal with THEIR hurt first, then later if you need to you can look at softening their communication if needed, when the incident is well past and you've already done the hard work to show you care about their feelings. But the actual issue is that you need to fix YOUR behavior that caused the problem in the first place. Shutting your partner down because you're upset they said anything to you at all is a positively childish approach to managing your relationship.
But then, a lot of people would just rather not hear it, and prefer partners that just keep their issues to themselves, even when "their issues" is about their partner being an insensitive jerk.