It is not about imposing our beliefs on others, as some claim: “Don’t let them tell you that. We don’t impose anything, we propose; we propose … a better way of living, a better way of life. It’s the great proposal.”
The culture battle is, as is any just war, one of self-defense, the defense of our families, our society, our way of life, our freedom and the legacy we leave our children. The battle needs to be fought because undermining vital foundations of our good society will harm people, especially children, undermine truth, threaten our freedom, and, crucially, threatens to keep people away from Jesus Christ, which is their single greatest need.
Some further reading.