Recapitulation theory is not supported (Talk.Origins)
The biogenetic law that ontogeny recapitulates phylogeny (that is, that the embryological stages of a developing organism follow the organism's evolutionary history) is false, yet embryological stages are still claimed as evidence for evolution.
(Talk.Origins quotes in blue)
1. Haeckel's biogenetic law was never part of Darwin's theory and was challenged even in his own lifetime. Haeckel himself did not necessarily advocate the strict form of recapitulation commonly attributed to him
This is not relevant, since recapitulation is still used as evidence for Evolution despite being proven false. Labels such as gill slits, yoke sacs, and tails are still applied to structures that serve totally different purposes despite those labels' being proved erroneous.
2. Irrespective of biogenetic law, embryological characters are still useful as evidence for evolution (in constructing phylogenies, for example), just as adult characters are.
However in both embryological and adult characters, one has to assume Evolution to construct phylogenies. In both cases common characteristics can only be considered evidence for Evolution if one assumes Evolution to begin with, since they only suggest relationships within Evolution theory. From a design standpoint it makes sense that a single designer would reuse not only parts but genetic programming instructions as well; this is done in human design all the time.
Furthermore, there is some degree of parallelism between ontogeny and phylogeny, especially when applied only to individual characters.
Some degree of parallelism between embryological development and theoretical Evolutionary phylogeny is not unexpected. According to Evolution, life started with single cell organisms, and most multi cellular organisms start out as a single cell, so some degree of parallelism would be expected between the two.
Various causes for this have been proposed. For example, there is selective pressure to retain embryonic structures that are needed for the development of other organs.
The simplest most likely explanation for the degree of parallelism that actually exists is the fact that both involve going from a single cell to a complex organism. The most important difference though is that embryological development is a real process resulting from a preprogrammed plan of development while Evolutionary phylogeny is a purely theoretical process with no plan at all.