Two reasons our white flowering dogwood (Cornus florida) hasn't bloomed some years were age and not enough water during the late summer heat. We grew ours from a sapling as an understory of live and red oaks where it took 5 or 6 years to start blooming - it is VERY slow growing in this location, so would probably be faster with a bit more light and in its native region. Our mildly alkaline prairie clay is west of the acidic forest soils it prefers.

One weekly deep watering with the lawn is not enough for our location and soil type during the triple-digit temperature runs in August and September - even in its shady location. If it's not given additional water fairly soon after the leaves start turning brown from the tips, it won't set buds in the fall. We've been caught twice forgetting to have this covered while on vacation and ended up with none or just a few "flowers" in the spring.

I will make sure it gets extra water at the end of summer and I am going to fertilize it too. I just am confused as to why the pink one bloomed and the white one didn't. They are both in the back yard but different areas. I guess I will have to wait until next year to see if extra water and fertilizer works.

Cornus florida varieties usually take a few years to begin blooming. Is is possible that your pink one is another Cornus cultivar/hybrid (kousa, nutallii,...) or maybe older than your white one?