Oh goodness, you're not failing! All babies are different. The occasional baby does sleep 7-7 from an early age. I'd say most take a lot longer to get into this pattern - some take years and years. Please please don't blame yourself.
I seem to recall reading that "sleeping through the night" at that age really means sleeping for an uninterrupted stretch of 5+ hours, so if you've achieved that you're winning! But even if your baby still wakes up every 3 hours it's perfectly normal, and could continue for many months yet.
I have a 6 month old. At 3 months she went to sleep around 6-7 p.m., slept until about 2 a.m., had a feed, went back to sleep, then woke again around 4 a.m. for a feed, then back to sleep. Not bad, I thought! Then the 4 month sleep regression hit and we were back to 3+ night feeds and 4.30 a.m. wakings for a while. It's gradually getting better though. Last night I did 1 night feed and got up at 5.30 a.m. - I feel like a new woman!
Anyway, don't beat yourself up. There's nothing wrong with you or your parenting if your baby needs to wake in the night, particularly for a feed. Being a good mother means responding to the baby you have and their needs, not conforming to an unrealistic stereotype.
Hang in there. It will get easier!