Why cannot DNA pass through cell membranes?

Hint: DNA is the genetic material that carries hereditary information. It is hydrophilic in nature. Cell membrane is a selectively permeable membrane made of phospholipid bilayer. Each phospholipid molecule has two hydrophobic tails and a hydrophilic head. The hydrophobic tails face towards each other, and the hydrophilic heads face outwards. It allows small substances to pass through easily.

Complete Explanation:
Cell membrane contains both proteins and lipids. It is a phospholipid bilayer wherein the hydrophilic head faces outwards, towards the extracellular matrix and hydrophobic heads face one another within the transmembrane portion. In accordance with this model, any substance to be ready to enter the cell must be lipid soluble so as to pass the hydrophobic tails within the transmembrane portion. DNA is also hydrophilic in nature so it is energetically unfavourable for the hydrophilic DNA to push themselves through the hydrophobic centres of the lipid bilayers.
DNA contains a sugar phosphate backbone, which makes it hydrophilic in nature and doesn't allow it to pass through the cell membrane because cell membranes are made from lipid bilayer which is hydrophobic in nature and pass lipid soluble molecules. But DNA is hydrophilic in nature which means water loving and soluble in water as solvent.

Note:
Human cells or eukaryotic cells hold their DNA within the nucleus which, just like the cell membrane, is a lipid bilayer. A lipid bilayer forms naturally when a group of amphipathic molecules (the phospholipids that structure cell membranes) encounter water. This lipid bilayer isn't hydrophilic all the way through. The nucleic acids are hydrophilic, they cannot cross this barrier as they are not lipid soluble.