There are no animal species that do not age. Some age slower than others.
I agree we should try to improve human lives, now and in the future, and extending healthy lifespan is certainly part of that. But there is plenty of reason to face the fact that we will all eventually die.
You'll see in that post that there are several species for which we find that mortality does not increase with age, i.e. they do not appear to age.
Now, I am not a specialist on the subject, so I will not be able to go into debate whether this is truth or fiction, but I have heard/seen this mentioned in several sources.
It is inevitable that a time will come where it will be possible for humans to stave off aging to a significant degree. Whether this is in 100 years or 10,000 years, it is difficult to tell. What measures should be taken because of this is for the future to decide.
I agree we should try to improve human lives, now and in the future, and extending healthy lifespan is certainly part of that. But there is plenty of reason to face the fact that we will all eventually die.