So if you think a 13 year old can give informed consent then why not a 10 year old? 8 year old? Why can't children give consent as soon as they intellectually know what the word means?
13 represents roughly the age at which most people reach a landmark of sexual development and awareness, and begin to understand and seek out sex for enjoyment. 8-10 year olds OTOH are typically not pubescent and therefore physically incapable of having intercourse in an efficient or pleasurable manner. The difference is that the 13 year old is likely motivated at least partially by pleasure and romantic attachment, while a prepubescent child is in most cases being coerced.
There is nothing about sexual maturity that enables good decision making, pubescent children have no significantly greater cognitive abilities than prepubescents.
There is nothing about human cognitive, emotional and physiological development that guarantees one will have the capacity to make good decisions at any stage of life. Referring specifically to females, a majority of adult women who consent are no less vulnerable to manipulation than a mature adolescent, and certainly not in any rational position to deal with the consequences of something going awry.
The "derp derp, puberty" argument doesn't work and purely as arbitrary as the line it seeks to replace. If anything pubescent children are at higher risk of undesirable outcomes from sex.
Puberty is less arbitrary than a rigid, all-encompassing age of consent law. But this is the type of issue that needs to be analyzed and judged on an individual basis in order for meaningful conclusions to be drawn.
