It's right there in the verse itself (if you don't just read the first half in isolation).
It's referring to God not going back on His promises to Israel even though they had been extremely disobedient.
The "therefore" means because or on account of.
Because GOD does not change.
On account of GOD does not change.
GOD's character (His innate being) won't change, and therefore His oaths can always be counted on.
So I'm not seeing the problem with what BR believes ---- that GOD does not change.
Ya'll seem to be a little overcritical of him.