If God is so loving why did he permit Adam and Eve to eat the fruit and ruin their lives and ours?

You kind of have answered the question yourself. It is exactly because God is loving. God did not create us out of his neccesity but rather out of his great love. Since we are created out of love God has endowed us with free will (CCC 1730). Now what is free will? It is simply the elective power given to human beings by which they can decide between choices put in front of them. One example of such a choice would be either to do good or to do evil. 

Why is free will necessary? 

Free will is necessary because in the absence of it we would be nothing more than puppets in the hands of the puppeteer. Everything that we do, even loving God with all our heart, would be a forced act. Now, that doesn’t sound like love, does it. 

As we have established that we do have free will and seen why it is necessary for us to have free will, let’s move on to see what comes along with free will – responsibility. Freedom makes man responsible for his acts to the extent that they are voluntary (CCC 1734) and every act directly willed is imputable to its author (CCC 1736). Which means that we are responsible for our own actions. This is why God asks Eve after the sin in the garden: What is this that you have done? He asks a similar question to Cain: What have you done?

So in the end we can say three things:

1. God has created us out of love
2. Since we are created out of love, he has endowed us with free will and
3. With free will comes personal responsibility

Coming to the question, if God had somehow not permitted Adam and Eve to eat from the tree, he would have two options before him:

1. He could either not give them free will or
2. He could have stopped them from eating the fruit in some other way for eternity

The first option is not possible as we know that to be made out of love means that we are endowed with free will. As for the second option, it would again mean that though Adam and Eve had free will, they did not have the power to exercise it. Which again, in ways, is equivalent to not having free will. It would be similar to a scenario where we are given a gift and asked never to open it. Both these scenarios are not logical. 

Imagine a household where the parents do not allow their children to do anything all by themselves out of their love for them. We surely can see how this would turn out for the children. 

This leads us to the conclusion that it was out of his everlasting love for Adam and Eve that he did not interfere in their actions (namely eating the forbidden fruit), because if he did, he would be acting against his own nature, that of love.