HopALongOn, what happens when your employers cuts your wages? When you have no strength to negotiate on anything that affects you at work, because you are one solitary voice. When you join a union, you become part of a collective, one that fights for each and every member.
You use the collective bargaining power of that union of people, to match the power that organisations have.
You don't have to support the strike, but by crossing the picket line you undermine the right of others to strike, you are telling your employer that it's ok to carry on, that you will support their actions. You also tell fellow employees that their concerns are of no consequence to you, people remember this when you want them to take action for something you believe in.