People don't fail, processes do.
Telling someone, "It's not you, it's me," when ending a relationship is disingenuous.
But telling someone struggling to perform their job that it was you, the manager, who failed, is usually right.
Internally, this means that we recognize that people don’t fail, processes fail. If a team member is floundering, something went wrong in one of our processes (recruiting, screening, onboarding, goal-setting, managing, etc).
OK, so you didn't fail as the manager, but the processes you employed to support your team member could probably use some serious work.
So, the next time you start to think or say that one of your team members isn't cutting it, look in the mirror first and consider whether your recruiting process was well-designed in light of your strategy, how well the onboarding process set your team member up for success, and what processes have been available to the team member to develop and excel.