Muslims often argue for the unity of God from the viewpoint that more than one God would bring chaos and fighting between the gods.
This is true if we think of many separate gods, but Christians only believe in ONE God, not many gods. But we believe that there is more "inner structure" to the Godhead that a unitary one.
The following explanation is actually a very classical one used by St. Augustine in his book "On the Trinity" [De Trinitate] in the 5th century.
We read in the Word of God, in 1 John 4:8 that "God is Love".
What are the necessary conditions that this can be a true statement?
For any event of "love" we do need the subject who loves, we need an object which is loved, and we need an expression of this love in some way, i.e. an interaction between the first two.
I cannot love when I am "just by myself". Focussing only on myself is egotism, not love.
Now, how can God BE Love if he was solitary in "unitary aloneness" from eternity past? None of the attributes of God are dependent on his creation. If God could only start loving after he had created us then his attribute of love would be dependent on us. He would not be self-sufficient in his attributes. But if he is unitary as Muslims believe, then love necessarily cannot be an attribute of his [nor can justice or mercy or any other relational attribute] because he is not in any relationship for eternity before he creates.
If God is not relational, how would he come to the idea to create anything ? How would he come to the desire to have an extension of his relationality beyond the Godhead if relationality is not part of his nature/attributes?
No, we all believe God created and he communicates with his creation. God is a communicator. God is love. But this can only be if he is love from eternity and hence there must be some relationality and expression and exchange of love within God himself.
That is where the trinity [or some kind of plurality] becomes philosophically necessary for God. Yes there is one God only but this God is love and is relational. And hence there needs to be "interaction of giving and receiving within the Godhead". That is why we need something like the Trinity.
Augustine then says that Father and Son are eternally in love with each other, giving and receiving, and that the Spirit is maybe like the personalization of this 'dynamic relationship', the transporting the love of the one to the other.
Note again: This is a model, an analogy again. No analogy is perfect. But think about it, and let me know how you think God can have relational attributes if he was a solitary unity from eternity past.
[This was a very quick and sketchy few paragraphes, any of my Christian brothers and sisters who would like to improve on this, is most welcome to do so. Just send me the article and I will put it up.]
On the Trinity