I just finished reading an article by Kostas Kampourakis and Alessandro Minelli, "Evolution Makes More Sense in the Light of Development," in the journal American Biology Teacher. Here’s an outline of the authors’ argument:
Intuitions of design and of essentialism (the idea that entities have essences) arise during early childhood and persist into adulthood, making evolution seem counterintuitive and difficult to understand. Even though we know evolution is true, childish misconceptions get in the way of students’ acceptance of it.
Evolutionary developmental biology (evo-devo) can help students understand why essences are not fixed (because development can be affected by the environment and eventually evolve), and why organisms are not designed (because they exhibit peculiarities produced by their evolutionary histories).
Evo-devo addresses the problem of macroevolution in terms of "evolvability," defined as "the capacity of a developmental system to evolve." The question of how adult form A evolved to adult form B can be answered by realizing that some elements of their developmental processes are common and that minor changes in molecular networks can have significant morphological effects.
In summary, "If it is difficult to conceive how evolutionary change is possible because one cannot understand that changes in ‘essential’ properties are possible or because structures seem to have been designed …, evo-devo helps explain with concrete examples that organisms can change significantly through minor changes in their genomes and acquire new structures in the course of evolution."
Note that evo-devo’s "concrete examples" — other than mutations that produce monstrosities such as fruit flies with legs growing from their heads — consist of (a) comparing separate species that differ in a particular morphological feature, (b) identifying differences in the expression of developmental genes correlated with that feature, then (c) concluding that the feature evolved because of changes in the expression of those genes.
If not, just leave your childish intuitions behind and accept evolution like a grown-up. The rest is easy.