Why is it that antibiotics lack inhibitory activity against eukaryotic cells such as fungi?

Anti-bacteria: The term "antibiotics" specifically refers to medications developed against bacteria, which are very different than fungi. We call those medications 'antifungals'. During the R&D of drug development, an agent is analyzed as to 'what' its activity is against a certain microorganism, while balancing any harmful affect against human cells. That is the selective design of these medications.

Targeting: If an antibiotic targets a protein that is only essential to prokaryotic cells, then in eukaryotic cells, it will not work as an antibiotic. It is all about the right drug working against the right target in the intended organism.

Different organisms: Antibiotics aren't effective against eukaryotic cells because they don't chemically bind with their cell walls or rna. As a matter of fact penicillin is actually produced by a fungus. Antibiotics are developed and synthesized to act specifically on bacterial cell walls and RNA to inhibit protein synthesis.