Can you miss an attack on purpose, and have it count as having made an attack?

Question

For example, if one wanted to trigger the benefit of the Mobile feat, wherein you can move away from a creature you made an attack against without provoking an opportunity attack, can you choose to miss the attack on purpose?

The mechanical benefit of this over taking the Disengage action would be that you can use the rest of your attacks from the Extra Attack feature, or still use TWF's bonus action, or potentially save an "on next hit" ability or effect for a different non-adjacent creature on the same turn without taking an attack of opportunity from, or damaging, the currently adjacent creature.

Answer 1

No, you can't.

I will essentially replicate my answer from here: Can I choose to fail the ability check for Dispel Magic?

5e works based on three steps.

1. The DM describes the environment.
2. The player describes what they want to do.
3. The DM narrates the results of the adventurers' actions.

Here, we are working in Step 2. If you choose the Attack action, what you want to do is attack - and hit - a creature or object. That's what your character wants to do - actually attack. If you choose that action, you can't choose to miss.

On the other hand, if you choose the action "pretend to attack", you did not attack, thus features that depend on actually attacking will not trigger - that is a completely different action.

Essentially, your character has no concept of an action which would be "make an actual attack, but force a miss" - either it makes an actual attack or it pretends to attack and misses, but again, these are different actions and only one is the Attack action defined by the rules.

As Gandalfmeansme mentioned, though, you can force yourself to bad luck using improvised weapons, which you are not proficient with (and as a Monk, you will be using Str instead of Dex, which might as well be a dump stat), and throw yourself in the ground for disadvantage (or, depending on how your DM rules it, just closing your eyes before attacking and being subject to Blinded condition).

Answer 2

Sort of...

You could certainly pretend to attack a creature, but really attack a space two feet to the left of them, and make it look like you meant to hit them. That's no problem. But you're unlikely to convince a DM that this should trigger a feature that happens when you attack that creature, since it's hard to make the argument that you have actually "attacked" them. There's guidance for what is and isn't an attack in the PHB (p. 193-194):

an attack has a simple structure.

1. Choose a target...
2. Determine modifiers...
3. Resolve the attack...

If there’s ever any question whether something you’re doing counts as an attack, the rule is simple: if you’re making an attack roll, you’re making an attack.

If you chose to target a space near the creature, then you haven't targeted the creature, so by the above definition you didn't attack it. If you want to attack the creature, you must target it, determine modifiers (mostly done by the DM), and make an attack roll. And if the attack roll succeeds, you hit it.

However, step #2 above permits you to do some things that could likely result in a miss. For example, you could deliberately make an attack with an improvised weapon (such as by making a melee attack with a weapon that has the ammunition property): this would mean you don't add your proficiency bonus to the attack. You could also take steps to ensure your attack has disadvantage (such as by going prone before you make the attack). These decisions couldn't make a hit impossible (at very least, you could roll two natural-20s), but they would make a hit much less likely.