Try any of the following instead:
paste(my[[1]], my[[2]])
# [1] "1 10" "2 10" "1 11" "2 11"
paste(my[, 1], my[, 2])
# [1] "1 10" "2 10" "1 11" "2 11"
paste(my$m, my$y)
# [1] "1 10" "2 10" "1 11" "2 11"
do.call(paste, my)
# [1] "1 10" "2 10" "1 11" "2 11"
The problem is that you weren't actually selecting the values in that column, but rather, a single-column data.frame
.
Of course, you could just use your original vectors:
> paste(m, y)
[1] "1 10" "2 10" "1 11" "2 11"