Upwards of 95% of the time, playing Aether Vial on turn one is going to be correct. It rarely matters if you are on the play or on the draw, jamming Vial is usually your best play. The upside of it resolving is so strong that it usually outweighs the other options. It makes your sequencing for the rest of the game much easier and allows you to dedicate more of your resources towards disrupting your opponent. Below are some examples of the times when this rule may not apply. You will notice that many of these scenarios have a large number of conditional statements attached; that is no coincidence, as you really have to work to come up with scenarios where Aether Vial isn’t correct. This isn’t an exhaustive list, but it should help you get the general idea of times where other options might be better.
Scenario 1: Your opponent is on the play, fetches, and casts Deathrite Shaman. Your hand contains Swords to Plowshares but does not contain Phyexian Revoker or Wilt-Leaf Liege.
When you are on the draw, the threat of a turn two Liliana of the Veil is terrifying. Preventing that is often a priority. Even here, depending on the contents of your hand, it is perfectly reasonable to still play the Vial and hope your opponent does not have Liliana. If you have a Phyrexian Revoker, playing the Aether Vial is definitely fine. Your opponent can cast a Liliana, but you can prevent it from getting out of control with the Revoker after one activation. If your opponent does not have a Liliana, you can revoke the Deathrite, priming yourself for a turn three Swords to Plowshares plus another two drop.
Scenario 2: Your opponent is on the play, did not mulligan, and casts Glistener Elf. Your hand contains Swords to Plowshares.
Against Infect, I’m all about not being dead. That deck needs four cards to kill you on turn two: a green-producing land (must be a forest), Invigorate, Berserk, and Glistener Elf. They have enough mana to cast one cantrip to dig for the missing piece and still kill you on turn two. As such, playing the Swords is probably just better. Now if your opponent has mulliganed, there is a higher chance that you will live to see turn two (especially if they scry to the bottom), meaning there is some merit to waiting until turn two to cast the Swords to play around Daze. That line, however, does not necessarily play around Force of Will or Vines of the Vastwood.
Scenario 3: Your opponent is on the play with a turn 1-2 combo deck, mulliganed, scried the card to the top, played a fetchland, and passed the turn. You have Pithing Needle in hand.
This is a weird one. Your opponent appears to need the card on top of their library quite badly if they keep it and then take no action on their turn. Casting your Pithing Needle either results in them fetching away an important card or a one mana Stone Rain. Both of those scenarios are great for matchups where you just want to make it to turn two alive.
Scenario 4: Your opponent is on the draw with a combo deck that does not play -X/-X hate. Your hand contains Mother of Runes plus a key hate-bear.
I think of this one as the Belcher-scenario. Your Aether Vial does not matter. The game is decided by turn two, one way or the other. If your Mother survives to protect the hate bear, the game is over. Playing Aether Vial doesn’t really matter, as the fundamental turn of the game doesn’t involve its help at all.