Wally and Beaver show a bad example in carrying for a living creature when we never see that cute Airedale puppy from Captain Jack, again

I always just assumed they were too young to be expected to care for a puppy at that age.

And of course they covered for the disappearance of the puppy in a later season episode (the pigeon episode?) when Ward reminds the boys that they had a dog and had to give it up because they weren't taking care of it.

Right and in Pet Fair Ward mentions how Beaver didn’t take car of his pigeons (he never even touched his pigeons being sick and didn’t want more after they died) or dog?. Wally mentions how he even goofed up his goldfish. Good thing Mrs. Bennett came to get Poncho before Beaver goofed that up. Imagine if Beaver and Wally kept Nick the horse. June would be constantly using a shovel to clean the garage as the boys would find a reason not to work.

Oh I can just imagine June shoveling the garage clean. "Ward! Come here...I have something for you to do!"

That’s right Ward was a “sentinental” old farm boy so wouldn’t mind clearing out the used straw and bringing in fresh hay and oats.

I always just assumed they were too young to be expected to care for a puppy at that age.

And of course they covered for the disappearance of the puppy in a later season episode (the pigeon episode?) when Ward reminds the boys that they had a dog and had to give it up because they weren't taking care of it.

Then why did the grown-ups give the too young to be expected to care for a puppy a puppy? Just to mess with it for a time and learn that human get to do whatever they want?

I wish they would have kept him too. He was adorable.

Maybe they wanted to make Beaver completely incompetent/foolish so they decided to make him irresponsible with pets. But the thing is that everyone is smart in some way, he had a high score in his second intelligence test (although he forgot that he already took one in which Charles Frederics swapped the names on their tests). Beaver did say so himself that he was good at geography, so maybe he could have done something with that?