Why in the Old Testament was the man not allowed to go to war the first year of a marriage?
The only reason I can give for Jewish men not being allowed to go to war the first year of a marriage under the Law of Moses is what the passage itself says.
When a man hath taken a wife, and married her, and it come to pass that she find no favour in his eyes, because he hath found some uncleanness in her: then let him write her a bill of divorcement, and give it in her hand, and send her out of his house. And when she is departed out of his house, she may go and be another man's wife. And if the latter husband hate her, and write her a bill of divorcement, and giveth it in her hand, and sendeth her out of his house; or if the latter husband die, which took her to be his wife; Her former husband, which sent her away, may not take her again to be his wife, after that she is defiled; for that is abomination before the LORD: and thou shalt not cause the land to sin, which the LORD thy God giveth thee for an inheritance. When a man hath taken a new wife, he shall not go out to war, neither shall he be charged with any business: but he shall be free at home one year, and shall cheer up his wife which he hath taken. (Deuteronomy 24:1-5)
The specific reason given was so that he could cheer up his wife. While that may have meant that he and his wife could find enjoyment in each other’s company, it may also include the idea that he could get her pregnant. (Under the theory that many women look forward to raising children, perhaps.)
Keep in mind that the Israelites did not have a standing army, and especially not a volunteer force such as we have in the United States. Since every male between twenty and sixty was required to fight this provision may have been necessary to allow new families to grow. If they had a volunteer army, then this law might not have been instituted, because a man would have chosen to be in the army. If he married after joining, that was his choice.
Another reason might be found in the context. This law is stated immediately after a discussion of divorce. It might be deduced that this way to “cheer up his wife” was instituted in order to reduce the number of divorces. (Again, that could be related to the fact of mandatory army service.)