Fg Off Bloggs
Give the guy a break - it seems like an honest question for heaven's sake.
KC-10 Driver
I believe the other answer is that then-Royal Army rebelled against the Crown under Oliver Cromwell in the Civil War 1642-48, and then ran the country as a military dictatorship for a bit(1650-something - 1660 "Rule of the Generals").
When Charles II was restored in 1660, he took a pretty dim view of the institution that bumped his Dad off and kept him in exile, so there wasn't much interest in giving them the title "Royal" back again. The RN didn't rebel (and indeed, it was the misuse of taxes to pay for the RN, so-called "ship money" that led to the regicide), and so kept the appelation.
Obviously individual regiments can become Royal - Royal Green Jackets, Royal Tank Regiment, Royal Flying Corps....
Hope this helps - sure that others will correct any errors above.
S41