This is expressing oneself selectively, besides everyone needs their own personal space as encroaching on another too much causes friction (Prov 25:17).
Various activities are best undertaken privately. While the Bible specifically mentions giving, prayer and fasting as not being done in a way which draws attention to the initiator, these and other spiritual disciplines wherever possible should be done in secret as this indicates genuineness rather than from the motivation of pride and recognition (Mt 6:1-6,16-18). Personal matters are confidential and should not be spread into the public domain.
Once a secret is shared it can become public news
Paul had a private meeting with the church leaders (Gal 2:2). Some matters need only involve the decision makers who, in turn, can relay only what needs to be passed on to others.
God knows everything and we cannot hide from Him. There is nothing hidden that will not be revealed ultimately (Mt 10:26; 1 Cor 4:5; Heb 4:13). This can be both a comfort and a challenge to us. Many shameful things are done in secret and they should be exposed (to those involved) by the light of God’s Word so they can be rectified (Eph 5:8-14; 1 Jn 1:9).
The private parts of the human body should be kept adequately covered and not exposed in public but only to one’s partner and for any necessary medical purposes. Females particularly need to beware of the effect their revealed flesh can have on males.