Hardly relevant to the question. A hatchet is a tool, putting your hand in a fire would make you a tool
So what exactly do you do with your big axe then? If a small axe is only there to make us feel all rugged and manly, what would the large axe be compensating for?

A big axe is useful for splitting bigger logs and cutting down trees.
When i was a lad we had a wood burning stove, we used a pretty big axe to split logs, does a good job.
For a small axe if your the artistic type then i could see a use for carving.
In this instance though your likely to be using short soft blows.
If your using a small axe for splitting logs though something is very very wrong in my eyes.
First off a strong swing with a small axe is asking for problems as unless your kneeling down any deflection will be aimed directly at your legs.
Add to that the fact that a small axe isn't really going to be much use splitting big logs and you have to wonder, why would you bother splitting smaller logs?
Around the house i could see that being blokes we'd buy one "just in case" but to take one out hiking with you just seems to be a fundamentally flawed idea.
1/ Your lugging all that weight around
2/ If you want smaller wood then just find a smaller branch
3/ Carving with an axe while out in the wilderness alone just seems a bit daft to me
4/ Although a romantic notion in this day and age a real fire is a vast waste of resources in all but the worst conditions, a stove will cook and heat water better and if you've planned well and nothing has gone wrong you should be warm enough without a fire (in the UK in all but the worst conditions).
If you decide to take it up then I can thoroughly recommend a small axe and a mallet.
Being a bloke any excuse no matter how small is usually enough for me to buy a tool, with a small axe though i really cannot see the point.
Lots of anti-axe stuff on here, no need for one etc etc. This is a knife forum, most people don't REALLY need to go outdoors and practise using knives, but they do and they enjoy it, same for axes I say. The circumstances that led to this accident are pretty clear. If your drunk don't bother, if you don't know what you're doing then learn first.
I sometimes use a chainsaw, that's chuffing lethal, I guess I am a dickhead for using that as well.
There is no "anti-anything" here.
An axe is an extremely useful tool, i've used many in the past many many times and they are fantastic at what they do.
These small axes in my opinion though are pointless and dangerous.
If your not carving or making a long term shelter then i really can't see the point in taking one with you except for some sort of down the pub bragging rights.
Ohhhhh and this is not a knife forum as far as i'm aware
But since you bought it up, it's rare i bother taking a fixed blade knife out with me unless i'm out the night.
It's just too much weight and space to give up when a folder will do.
With regards drinking.
I agree 100%, but again to me it does come across being a bit sad that folks have to go out in the middle on nowhere to have a drink.
Me personally if i want a drink i'll have a drink, be it at home or down the pub.
I also think it's extremely dangerous to be drunk out in the wilds, yet reading a very very very small minority of posts on here it seems some are unable to sleep outdoors without a skin full.
As with the small axes i does strike me as kinda pointless.
Why exhaust all that time and energy going out into the great outdoors, finding a beautiful spot, creating a great spot for sleeping, then getting drunk
But then i've just been fixing my radio controlled cars so many would see that as being pointless and me as a jerk being 43 and still playing with toy cars.
So it takes all sorts i guess.