Why should we emphasize that God loves, forgives, and saves for his own glory?
Two reasons (among others).
1) Because the Bible does.
I, I am he who blots out your transgressions for my own sake, and I will not remember your sins. (Isaiah 43:25)
For your name's sake, O Lord, pardon my guilt, for it is great. (Psalm 25:11)
Help us, O God of our salvation, for the glory of your name; deliver us, and atone for our sins, for your name's sake! (Psalm 79:9)
Though our iniquities testify against us, act, O Lord, for your name's sake; for our backslidings are many; we have sinned against you. (Jeremiah 14:7)