Q.Why is the law of segregation also called the law of purity of gametes?

'Gametes are never hybrid' describes the clean separation of paired alleles into different gametes -- the Law of Segregation.

Working

Mendel's three principles, applied to a monohybrid cross (a single gene with two alleles, e.g., T = tall, t = dwarf, in a heterozygous Tt plant):

• Law of Dominance: in the heterozygote Tt, only the dominant allele T is expressed in the phenotype (the plant looks tall), while t remains masked.
• Law of Segregation: during gamete (meiosis) formation, the paired alleles T and t, which lie on homologous chromosomes, separate from each other cleanly, so that each individual gamete receives only one allele -- either T or t, never both together in the same gamete. In other words, a gamete is always 'pure' for a given gene, never a hybrid combination of both alleles; this is why Mendel called it the Law of Purity of Gametes.
• Law of Independent Assortment (from a dihybrid cross): alleles of DIFFERENT genes located on different chromosome pairs segregate independently of one another into gametes.
• Law of Random Fertilization: any male gamete has an equal, random chance of fusing with any female gamete, which is what generates the predictable Mendelian phenotypic ratios (like 3:1 or 9:3:3:1) in the next generation.

The phrase 'gametes are never hybrid' is specifically about a single gamete never carrying both alleles of a gene together -- this is exactly the Law of Segregation.

"Gametes are never hybrid, they are always pure" is a statement of Mendel's Law of Segregation (Law of Purity of Gametes).

Working

Mendel proposed three fundamental laws of inheritance based on his pea plant experiments. The Law of Segregation states that an organism carries two alleles (factors) for each trait, one inherited from each parent, and that during the formation of gametes (meiosis), these two alleles separate (segregate) from each other so that each gamete receives only ONE of the two alleles, never both together.

Because a gamete carries only a single, unmixed allele for a given gene -- never a combination or "hybrid" of both parental alleles -- this law is often summarised in the classical statement: "gametes are never hybrid; they are always pure" -- hence its alternative name, the Law of Purity of Gametes.

This is distinct from the Law of Dominance (one allele masks the expression of the other in a heterozygote) and the Law of Independent Assortment (alleles of different genes assort independently of one another during gamete formation), neither of which specifically addresses the "purity" of individual gametes.