Why are most mutations in eukaryotic cells neutral? i.e. have no effect on the phenotype.
Your premise that most mutations in eukaryotic cells are neutral is dependent on where in the genome the mutations occur. Most of the genome of eukaryotes is non-coding, so mutations are frequently neutral unless they occur in some signaling region. In protein coding genes, all mutations in 2nd codon positions, and about half of the mutations in 3rd and 1st codon positions change the amino acid, and this is most often deleterious. It is informative to distinguish between mutations and substitutions. Many mutations are never observed because they are lethal. Substitutions are mutations that have survived the filter of selection long enough to be observed. Lethal mutations are never observed because they kill the embryo before it is born. And seriously deleterious mutations are removed from the population quickly as well. So selection acts to favor the observation of neutral substitutions, but most mutations are deleterious.