€4549 minus 21% VAT comes in around $4240.
Is VAT %21 percent of the final price (inclusive), or is it %21 added to the pre-tax price (exclusive), which would make it ~17.35 of the final price? You did that calculation as if it were inclusive, not exclusive.
[Equivalently, if the 21 percent is inclusive, it's equivalent to a 26.6% exclusive tax, in the US it would be like buying a $100 dollar item (our stated prices do not include tax) and getting $26.60 added to it at the cash register; 26.60 is ~21 percent of 126.60.]
Starting with his claim that €4600 is the price and is equivalent to $5400 (implied exchange rate of €1 = $1.174):
An exclusive computation takes $5400 and divides by 1.21 to get $4462 pre-tax. This is almost a thousand dollars less than the price paid. It's $562 above the US pre-tax price ($3900).
An inclusive computation takes $5400 and multiplies by .79 (taking 21 percent off the total) and yields $4266, which is $366 above the US pre-tax purchase price.
So basically all but either 366 or 562 dollars (or the equivalent in Euros) of the nominal price difference is due to the VAT (depending on whether the VAT rate is inclusive or exclusive).
That's why I said his complaint is with Europe. In fairness I should have said
mostly with Europe. Comparing apples to apples, the price in the US (before tax) is closer to the European price (before tax) but once taxes are applied, the difference is much, much larger; he's paying $5400 whereas I paid $4221.75