The strongest argument I find is that God gives spiritual gifts, I believe God can give a woman the skills/gifts to be pastor. Keep in mind that women also pray to God about this issue before becoming a pastor, and wait for His answer. Another compelling reason I find is that the Bible says single unmarried men cannot be church leaders:
1 Timothy 3:2 “A bishop (elder) then must be blameless, the husband of one wife, temperate, sober-minded, of good behavior, hospitable, able to teach”;
1 Timothy 3:12 “Let deacons be the husbands of one wife, ruling their children and their own houses well”; and
Titus 1:6-7 “. . . appoint elders in every city as I commanded you—if a man is blameless, the husband of one wife, having faithful children not accused of dissipation or insubordination...” These three passages suggest that an elder or deacon must be a married man.
However, if that's the case even Jesus and Paul would be unqualified to be pastor.
The authority issue is about the husband and wife relationship; the husband has authority over the wife. However, any random man does not automatically have authority over a woman. If the woman is married, I do think she needs the husband's approval before being pastor. My observation with the female pastors I see is that the husbands are proud of their wives.