Expelliarmus is a basic, low level, primitive spell. Well known, easily countered (shield, block). It's also not harmful, so if it misses/is blocked, you wasted "a turn", so to speak, allowing your opponent to attack unmolested.
As the old saw goes, the best defense is a good offense. Starting a duel with an offensive spell seems to make a lot more sense - if it connects, you progressed in the duel; if it doesn't, the opponent was busy countering it.
Imagine this game theory scenario breakdown:
"Counter" means shield or dodge/block
"Exp.OK" means Expelliarmus of yours that succeeded
"Exp.FAIL" means Expelliarmus of yours that failed.
Note that due to Expelliarmus's basic nature, the chances of it succeeding is always HIGH on both sides, unless the opponent blocks (then chances are low instead, again due to basic nature)
You: Opponent Result Probability Advantage
Exp.FAIL Counter (success) Status Quo High None
Exp.OK Counter (failed) Opponent disarmed Low You
Exp.OK Exp.OK Both disarmed High None
Exp.OK Exp.FAIL Opponent disarmed Low You
Exp.FAIL Exp.OK You disarmed Low Opponent
Exp.FAIL Exp.FAIL Status Quo Low None
Exp.FAIL Weak Offensive You suffer effects Low Opponent
Exp.OK Weak Offensive Opponent disarmed+ High None
You suffer effects
Exp.FAIL Strong Offensive You hurt/dead. Low Opponent
Exp.OK Strong Offensive Opponent disarmed+ High Opponent
If you open with Expelliarmus:
- If the opponent opens with a block/shield/dodge, most likely, it's a wash. No advantage to anyone
- If the opponent opens with Expelliarmus, most likely, it's a wash. No advantage to anyone.
- There's a small chance that you disarm them and they fail to disarm you. Due to the basic nature of the curse, that's unlikely.
- If the opponent opens with a weak curse, they are most likely disarmed but you are hurt. This is a wash - you can recover from a weak curse; and they can retrieve their wand.
- If the opponent opens with a strong/lethal curse, they are most likely disarmed but you are severely disabled/dead. Fat lot of good it does you to have them disarmed in exchange.
in a real duel (where the goal is to take out the opponent), the BEST strategy to counter Expelliarmus is to fire a strong offensive curse, and it's a stably winning strategy. Thus, Expelliarmus is a very bad opening.
In non-real school duel, most likely outcomes are ones with no-win or opponent win. The only outcomes with your advantage are those that have very low probability (opponent shields but shield fails; and opponent casts Expelliarmus which fails). So, Expelliarmus isn't really worth it, it's a wash at best as an opening. And the school duels are mainly training for real duels so aquiring bad habits from early on is a Bad Idea.