Lamarck's theory is rejected because it does not explain how traits are inherited through the passing on of genes.
Explanation;
According to Lamarck's theory the mechanism for evolution involved the inheritance of acquired traits.
Lamarck believed that traits changed or acquired over an individual's lifetime could be passed down to its offspring.
However, this theory was dismissed based on two things; first through experimentation, such that changes that occur in organisms during life are not passed on to the their offspring.
Additionally, the study of genetics also proved the Lamarck's theory wrong, which explained that traits are passed on through genes, which are not affected by the outside world.