The algorithm is bad: it's complicated and slow.
The competing algorithms were much simpler, much more secure by construction, and much faster. Most importantly, there was no obvious way to backdoor the competing algorithms, but there's a hilariously trivial way to backdoor Dual_EC_DRBG.
Ergo: the only reason you would ever devise or use Dual_EC_DRBG is to introduce a backdoor capability. There is no other believable benefit or reason.
But rest assured, the NSA promised that they destroyed all copies of the private key they used to generate the public key for Dual_EC_DRBG.
Oh wait, you thought you could generate your own pair and throw away the private key? Ha-ha... haaa. No. That's not compliant with the "standard", which the NSA forced upon the industry, and/or literally bribed companies with millions of dollars to accept willingly.
It's as obvious a backdoor as you could possibly have.
Even if the NSA didn't use it as a backdoor -- I'm crying with laughter now -- the Chinese hacking group APT5 definitely did: https://blog.cryptographyengineering.com/2015/12/22/on-junip...