You’re viewing it as similar to this:
I have £10
On the toss of a coin I’m offered double or half so I should do it.
In the this case double or half is two different amounts £5 or £ 10 so I can gain more than I can lose.
Not so wrt the two envelopes.
Initially, you have nothing.
You selected an envelope but you don’t know whether the envelope you selected has £10 or £20 or whether its amount is larger or smaller than the other envelope.
You selected an envelope with £10 in it. On switching you have £20 in the other envelope
You selected an envelope with £20 in it. On switching you have £10 in the other envelope.
You end up with either £20 or £10.
Now, if you selected the £10 envelope and did not switch, you have missed the opportunity to get another £10. (100% gain)
OTOH, if you selected the £20 envelope and did not switch, you have avoided the loss of £10. (50% loss)
You end up with either £10 or £20.
However, the order of £10 and £20 is reversed wrt switching and not switching.
So, why switch if the final outcomes are £20 or £10, £10 or £20?
That might be the actuality for one instance, but what about multiple instances?
Because you don’t know what is in both envelopes and the odds are even, the guide to switch or not to switch is the expected value:
Where A is the amount in the selected envelope.
Whether A is £10 or £20, the expected value is more than A ....... you gain on average by switching.
If there were multiple instances of choosing the two envelopes, you gain on average by switching which means that there will be more £20 verses £10 outcomes and vice versa for not switching.
Paradoxically, this is recommended ad infinitum in steps 9, 10 and 11.