Is ebola non-contagious until symptoms appear? Why?
First, confirmation from the World Health Organisation:


  The incubation period, that is, the time interval from infection with the virus to onset of symptoms is 2 to 21 days. Humans are not infectious until they develop symptoms. 


But


  People remain infectious as long as their blood and body fluids, including semen and breast milk, contain the virus. Men who have recovered from the disease can still transmit the virus through their semen for up to 7 weeks after recovery from illness.


They also state that deceased people may still transmit the virus via body fluids.

As to why the patients become infectious only when symptoms show, there are several related ideas.  For example, from the CDC:


  Ebola virus enters the patient through mucous membranes, breaks in the skin, or parenterally and infects many cell types, including monocytes, macrophages, dendritic cells, endothelial cells, fibroblasts, hepatocytes, adrenal cortical cells and epithelial cells. The incubation period may be related to the infection route (i.e., 6 days for injection versus 10 days for contact). Ebola virus migrates from the initial infection site to regional lymph nodes and subsequently to the liver, spleen and adrenal gland. 


According to Dr. Ray Schilling:


  Ebola virus disease has an incubation time of 8 to 10 days where the person may complain of some tiredness, but is not sick yet. This is the time when the Ebola virus multiplies. It  paralyzes the immune system and distributes itself through the organ system.


From there, the symptoms and effects of Ebola are fast, according to the article "Ebola Virus Pathogenesis: Implications for Vaccines and Therapies" (Sullivan et al. 2003):


  Ebola virus replicates at an unusually high rate that overwhelms the protein synthesis apparatus of infected cells and host immune defenses