Don't use $ in this case; use [ instead. Here's a minimal example (if I understand what you're trying to do).
mydf <- data.frame(A = 1:2, B = 3:4)
mydf
# A B
# 1 1 3
# 2 2 4
x <- c("A", "B")
x
# [1] "A" "B"
mydf[, x[1]] ## As a vector
# [1] 1 2
mydf[, x[1], drop = FALSE] ## As a single column `data.frame`
# A
# 1 1
# 2 2
I think you would find your answer in the R Inferno. Start around Circle 8: "Believing it does as intended", one of the "string not the name" sub-sections.... You might also find some explanation in the line The main difference is that $ does not allow computed indices, whereas [[ does. from the help page at ?Extract.
Note that this approach is taken because the question specified using the approach to extract columns from a matrix or data frame, in which case, the [row, column] mode of extraction is really the way to go anyway (and the $ approach would not work with a matrix).