Why
When the string is expanded, it is split into words, but it is not re-evaluated to find special characters such as quotes or dollar signs or … This is the way the shell has ‘always’ behaved, since the Bourne shell back in 1978 or thereabouts.
Fix
In bash, use an array to hold the arguments:
argumentArray=(-ir 'hello world')
grep "${argumentArray[@]}" .
Or, if brave/foolhardy, use eval:
argumentString="-ir 'hello world'"
eval "grep $argumentString ."
On the other hand, discretion is often the better part of valour, and working with eval is a place where discretion is better than bravery. If you are not completely in control of the string that is eval‘d (if there’s any user input in the command string that has not been rigorously validated), then you are opening yourself to potentially serious problems.
Note that the sequence of expansions for Bash is described in Shell Expansions in the GNU Bash manual. Note in particular sections 3.5.3 Shell Parameter Expansion, 3.5.7 Word Splitting, and 3.5.9 Quote Removal.