If Jesus' model for his followers and Paul's goal for churches was to dominate others, the word Paul received from Jesus ("My grace is sufficient for you, for power is made perfect in weakness" - 2 Corinthians 12:9) and Paul's final claim about himself ("For whenever I am weak, then I am strong" - 2 Corinthians 12:10) would make no sense. Clearly, their goals for us are not domination, but ministry. When your Savior saved through dying on a cross - a stumbling block for many then and now - humility and service and mercy and weakness become practices you seek and attributes you acknowledge, not avoid.
We acknowledge our weaknesses because it's honest to do so. The weight of trying to pretend we have it all worked out is too heavy.
We acknowledge our weaknesses because doing so drives us to turn to the Father, Son, and Holy Spirit and to our brothers and sisters in Christ for help. Turning to God and others helps that heavy load become more manageable.
We acknowledge our weaknesses because when we do so we become better ministers to others. If I think you haven't struggled, I don't want you to know that I have. If I can't imagine that you have weaknesses, I don't want to share mine. But, if I know that you have worked through some things, are working through others, and still have a ways to go on still others, I'll be more vulnerable with you and more open to you, and I'll trust that the Lord will be in the midst of our gathering of two or three in his name.
Acknowledge your weaknesses before God and, as it's appropriate, others. God's grace is sufficient and acknowledging where you are weak is actually sign of true strength!