Step 1: Concept
Noble gas reactivity depends on the ionization enthalpy. Lower ionization enthalpy (larger atoms like Xenon) allows for the formation of compounds with highly electronegative elements like Oxygen and Fluorine.
Step 2: Meaning
Neon ($Ne$) is a very small atom with an extremely high ionization enthalpy. It holds its electrons very tightly.
Step 3: Analysis
Xenon ($Xe$) is large and has a relatively lower ionization energy, allowing it to form stable fluorides ($XeF_{2}, XeF_{4}, XeF_{6}$) and oxyfluorides ($XeOF_{4}$). Neon, however, does not have any stable neutral binary compounds with fluorine under standard conditions because it is too small and stable.
Step 4: Conclusion
Therefore, $NeF_{2}$ does not exist.
Final Answer: (B)