SUMIF - not returning expected result

I have a table similar to below in columns A-D and Rows 1-4, but with many columns (this is simplified), I want the sum of all the data in columns with a column heading of x

I used this SUMIF formula: =SUMIF(A1:D1,"x",A2:D4) and expected the result to be 16 but got 3

Have I misunderstood the SUMIF function? What function should I use to get the result I was expecting?

x y z x
1 1 1 2
2 1 3 3
3 3 4 5