What I would like to know now is
on a technical level, WHY
you can safely re-use a receiving address
but not a sending address?
we are using cryptography to sign
the transaction and verify the
transaction... so why does
the address become known only
on the sending side and not
the receiving side?
The first thing you need to do is remove incorrect concepts like receiving and spending addresses. There is no such thing. There are only addresses. The protocol doesn't even use addresses it converts addresses to the raw PubKeyHash (which is a hash of the Public Key).
When you send funds to a given address you are actually sending it to the PubKeyHash. The transaction becomes a public record thus the PubKeyHash (and the address can be computed from it) is a known however the Public Key (PubKey) is NOT known. Look at the output of any transaction the funds are sent to a PubKeyHash (160 bits).
For example here is a recent tx (pulled at random).
http://blockchain.info/tx/4c555be716ccf923252ae118f2e9719a7ce6d4fdbf52a8cc03489b330debbd01Funds were sent to 1Fv1uSsxr8z4hCHi2yhzuLf2sQafJfLbF8
Technically the output is this
OP_DUP OP_HASH160 a3988fd05be9c9b642503e61ec6bb6ed553ab8a2 OP_EQUALVERIFY OP_CHECKSIG
a3988fd05be9c9b642503e61ec6bb6ed553ab8a2 is the PubKeyHash which corresponds to address 1Fv1uSsxr8z4hCHi2yhzuLf2sQafJfLbF8.
So the PubKeyHash is known and if you search the blockchain by address you will see this address received funds multiple times. However the PubKey is unknown. What is the PubKey for a3988fd05be9c9b642503e61ec6bb6ed553ab8a2? There is no feasible method of finding out (unless you already know because you have seen the PubKey.
Now if 1Fv1uSsxr8z4hCHi2yhzuLf2sQafJfLbF8 spends some but not all of these outputs then in the input side of the tx, to "prove" the outputs correspond to his keypair the user will provide the PubKey. The PubKey becomes known when it is spent because it is provided in the input side of the spending transaction. Until that happens the PubKey is unknown.
If tomorrow there was an exploit which required knowledge of the PubKey this user would not be immediately at risk.
Is this a feature of all the altcoins
as well?
If they were based on Bitcoin or a derivative of Bitcoin then yes. If they were completely new then it is possible this doesn't apply although I don't know of any.