Let me start by saying that I do not believe that morals are subjective. I believe that there are certain moral statements that we can make which are binding for everyone at all times. I won't be discussing those in this post or how I arrived at that position. I simply wanted that out of the way so that I am not accused of preaching something I am not.
There are a number of ethical theories which have been purposed for arrive at morals for individuals and society. Many of them don't compete as much as they try to offer better answers. In fact, a number of them can be said to supplement one another. That said, most ethicists push their theories as exclusive. But there is one that probably gets pushed as exclusive more than any other. That would be divine command theory. Most religions do this, but in America Christianity would be the religion that does the majority of the pushing. This is the religion I will address mainly in these posts if I address any at all.
The first line of attack Christian apologists will take is to point out that without a divine law giver morality is subjective and arbitrary. There are two problems with this. The first is that this is merely an assertion. Is it true that without a divine law giver morality is subjective and arbitrary? On the surface it could seem that way. But ethicists who have been wrangling with these ideas for centuries would certainly beg to differ. Typically, what the apologist is doing here is making a distinction between subjective and absolute morality, not subjective and objective morality. It is really objective morality we should be concerned with. It is true that some people believe in subjective morality, and a few years ago it was all the range at universities, but no one today takes it very seriously. It simply doesn't work and anyone, giving it even a modicum of thought, knows it. But here the apologist is being a bit dishonest because they are making it seem that the argument is about subjective vs. objective morality when he or she really isn't wanting to talk about objective morality at all.
The second problem is best summed up with the question, "so what?". As I stated in the beginning, I don't believe morality is subjective. If morality were truly subjective it would be a rather terrible situation. People would just being doing stuff because they wanted to do stuff, there could be no accountability and society would completely break down. Of course, subjective morality isn't even possible, but let's pretend for a moment that it is. So what? It doesn't follow that because not having a divine law giver means morality would be subjective therefore there must be a divine law giver. If morality is truly subjective, then it is subjective. The end. It is the burden of the Christian to prove there is a moral law giver. They cannot do this by pointing out what we would rather not have and show how having a god would make things better and then declaring "Here he is!" It simply doesn't work that way. You might as well ask a child if they would rather have a world with Santa or without Santa. Their answer won't prove Santa's existence, even if having a Santa would be ethically the best option.