You may have heard of people who feel rich, old, or powerful enough that they can speak their mind without caring about what people think. Sometimes, it's just an improper license to be mean; and sometimes, it's a refreshing honesty that everyone and every organization would do well to make sure they have access to.
As a Christian, I believe that speaking hard truths is important. To pull punches is to leave important things unsaid. And to speak hard truths in an insensitive way can be even more hurtful than keeping your mouth shut.
So how to thread the needle between these two undesirable outcomes? As always, my role model is Jesus. If you read the gospels with an open mind, you'll be surprised how many times He says things that seem pretty harsh. He certainly made a lot of enemies with His words. But He was also gentle and caring enough to be beloved by children, sinners, and outcasts alike.
I think being Jesus-like in speaking truth boils down to three things. First, Jesus' self-worth was firmly anchored in His relationship with the Father; it's what allowed Him to say and do unpopular things without factoring in what effect they would have on people's opinion of Him. Second, Jesus knew His mission as having been sent by the Father; and speaking truth was a non-negotiable, even if it meant riling up some and losing others. Third, Jesus' behaviors were captive to an overall value system, which was about humbling those who were improperly exalted and exalting those who were improperly humbled, and which was ultimately about correcting, healing, and restoring people towards right relationship with the Father.
An anchored self-worth, a mission understood, and a value system to frame it all. Easier said than done, but for me it provides a framework to speak truth in a way that is correct, neither lacking courage to say what needs to be said nor saying it in a manner that tears down rather than building up.