As stated for the question above here's an analogy:
You are a robber looking for a house to rob with two different scenarios that might occur.
1. You have a key that you know belongs to a house and you can use it to let you inside. However, you have no clue for WHICH house it belongs to. At any neighborhood and at any house, the key can be utilized for direct access for one undisclosed location you need direct access to. But because the location of the house is kept secret, you don't know where to look.
2. You are standing right in front of the primary target house. You do not have the key with you but you know there are ways of getting in the home. You can either break the windows, use a crowbar, or slam down the door. It may take a while but you have the necessary tools for the job (tools = BRUTEFORCE)
(For my thought process on this analogy, I'm thinking mostly on the idea of a message that's encrypted and released publicly. However, this is also for the encrypted algorithm as well.)
With these scenarios given, I wanna know why this doesn't apply for Symmetric Cryptography? (I am new to Cryptology, so my apologies if my thinking process for this is not entirely correct. Any help is appreciated.
EDIT: Did some further reading. Is the main reason due to key lengths being the reason why its hard to decrypt a message/algorithm? I just read for a key length being around 128 bits of length results in 340,282,366,920,938,463,463,374,607,431,768,211,456 possible combinations. This is what makes the key itself valuable to hold as it will takes years to even consider brute forcing it. So having the message/algorithm out in public would provide no possible danger if the key itself is difficult to acquire through brute force. Is this the reason why?