The use of such letters was common in mathematics long before programming existed. x, y, z were used as variables by Descartes in 1637; in his framework, a, b, c and other letters towards the start of the alphabet represented known values, letters towards the end of the alphabet represented unknown values. The use of i, j etc. doesn’t go quite that far back, but it was common at least for summation and other such operations, where the variables represent indices.
The original FORTRAN paper doesn’t give any specific arguments for the FORTRAN pattern, which is more than convention: variables in FORTRAN O could be of two types, fixed point (with a one- or two-symbol name starting with i, j, k, l, m, or n), or floating point (with a one- or two-symbol naming starting with any other character of the alphabet). Knuth notes that “the names of variables were restricted to be at most two characters long at this time; but this in itself was an innovation, FORTRAN being the first language in which a variable’s name could be larger than one letter, contrary to established mathematical conventions”. As can be seen in the rest of that paper, early programming languages closely followed mathematical representation, which explains the influence of the latter on the former.
There has been some amount of influence of computer programming notation on mathematical notation since then though; for example, some mathematical papers use words as variable names rather than single letters.