Why in nucleic acid replication one strand is ahead while the other strand is behind?

Because the leading strand is synthesized continuously while the lagging strand is discontinuously synthesized.

Explanation:

Two DNA strands have opposite polarity, that is, the 5' end of one strand lies opposite to the 3' end of the other strand. However, DNA replication can occur in 5' to 3' direction only since the formation of phosphodiester bonds require the presence of nucleophile 3' OH to attack the 5' phosphate of an incoming deoxyribonucleotide.  

The problem is solved by the synthesis of the leading strand continuously and the synthesis of the lagging strand in a discontinuous manner. Lagging strand synthesis requires the formation of primers and their elongation to form Okazaki fragments that may have few hundreds to few thousands of nucleotides. Removal of primers from Okazaki fragments is followed by joining them together to make the long lagging strand. The discontinuous replication of the lagging strand makes the replication at the leading strand ahead of it.  

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