1 Corinthians 16:13-14
13 Be watchful, stand firm in the faith, act like men, be strong. 14 Let all that you do be done in love.
The word translated here "act like men" is the Greek word andrizomai. In the Greek translation of the Old Testament this same word is often used where you see the charge, "Be strong and courageous!"
What does it mean to act like men?
Diffiferent people may have different ideas about what acting like a man should look like. But I think most agree that it involves something of accessing those things that make us and define us as men in comparison to the weaker sex.
Men are strong and are impressed by strength. Men are capable and inspire comfort and security by their confidence. Men are leaders, whether in battle or in confession. Men serve and spend themselves for the sake of those they love. Men die so that others may live.
Paul is telling the church at Corinth to act like men. He is not telling women to act like men. He is expecting the primary recipient of this charge to be the men of Corinth. He has already addressed gender roles and complementarianism in chapter 11 of 1 Corinthians.
The glory of God is by grace placed on men to serve Christ and in Him inherit His Kingdom.
I heard John Piper once say, "to be a man means you go down with the boat." A clear reference to women and children being the first candidates for the lifeboats and the men being the means by which said women and children are placed, protected, and secured in the lifeboats.
1 John 3:16
By this we know love, that he laid down his life for us, and we ought to lay down our lives for the brothers.