I've just been at a wedding and was reminded again of one of my favourite marriage verses: "He who loves his wife loves himself." (Eph 5:28).
It occured to me that Paul could not have said this the other way around. He who loves himself does not actually love his wife. In the marriage covenant, other-love is self-love. It's the only self-love allowed. But the reverse is not true: self-love is not other-love
Now think of God. If you really wanted to, you might want to talk about "God loving Himself." But of course you'd only do so in the same way you'd talk about a husband loving himself. How does a husband love himself? He lays down his life for his wife. How does God love Himself? The Father commits all things into His Son's hands.
Any talk of self-love in God must be explicitly talk about triune relations - the Father loving the Son in the Spirit. You simply can't talk about God loving Himself without emphatically underlining the multi-personal, other-centred nature of this God and this love. Otherwise you make Him like the selfish husband.
In trinitarian theology there's an old argument about how you should proceed. Should you "begin with the One" and then show how there are actually three Persons in this One God. Or should you "begin with the Three" and show how those Three are the One God?
Well surely we must acknowledge from the outset the tri-personality of this God. Or else all that you say under the category of "The One God" will start to sound like the selfish husband who, from the overflow of His self-centredness, manages to love another! So wherever we 'begin' three-ness must be on the table. (More on this here).
There is a way from Trinity to aseity. But there is no way from aseity to Trinity.