One of the reasons we should not be ashamed of the gospel is because it graciously reminds us that if there is a Savior for sinners, then there's no shame in admitting we're sinners in need of a Savior. The gospel frees us from feeling like we have to hide in the shame of our sin. It liberates us from having to suppress what we (and everyone close to us) already knows to be true, because admitting that bad news leads to savoring the good news. The dire nature of this bad news is what makes the gospel such gloriously good news.
And the sooner we realize this, the better.