Rest day= GAINZ Here's a funny video that explains it. NFSW. https://www.youtube.com/watch?v=0YtSaRl4fkU
Let's put it this way: if you don't need rest days, you're not exercising properly if you want to build up strength and mass. Also like Extra said it's the repair of muscle fibers which makes them stronger and rest is essential for that. If the repair is "interrupted" by another workout you're diminishing the gains. Nosein made good points too above. And I have to agree you'd think an ex-boxer would know this...