Why do we see only redshifts of distant galaxies, not blueshifts?
The shifting of light to lower energies or longer wavelengths (toward the red if we talk about visible light) from distant galaxies is caused by their recession from us under the universal expansion. There are other ways to affect light energies but they are less strong than the expansion. In addition objects moving not perfectly in step with the expansion flow will show Doppler or “peculiar” velocity shifts. In fact about 10 galaxies do show blueshifts since their expansion redshifts are smaller than their Doppler shifts. This only happens because they are so nearby that the expansion is weak; they only constitute 0.01% of all cases.