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I pass Salam a lot, almost to every man I pass by, but I when I say Salam (not to my father) when my father is with me, he gets angry and shouts at me, he says that if they wanted Salam they would have said it, and that I should say it to people I know, and some other excuses. Though his arguments are weak, but since he's my father, and kind treatment to parents is obligatory, should I stop saying Salam when he's around, since Salam is a (very recommended) Sunnah?

Initiating salam is Mustahabb while obeying father is Wajib, the latter takes precedence. Also remember the Hadith:

I asked the Prophet (ﷺ) "Which deed is the dearest to Allah?" He replied, "To offer the prayers at their early stated fixed times." I asked, "What is the next (in goodness)?" He replied, "To be good and dutiful to your parents" I again asked, "What is the next (in goodness)?" He replied, 'To participate in Jihad (religious fighting) in Allah's cause."

I recommend you not do it if it is not welcome by the receivers.

Unfortunately I have to say, one of the calamities that have befell the Islamic world is soulless adherence to the ritual without knowing their purpose and their underlying moral foundations. This happens when law is overrated against ethics and spirituality, (a shortcoming that is affecting most of us Muslims today, I believe!)

Saying salaam as a greeting in Islam is meant to be an opening message of peace, sympathy and kindness to your fellow humans, and as that it would have to come from a genuine attitude of peace and kindness in our hearts in which case it would be inevitably expressed in our mood, tone and bodily expression when uttering it.

So if the lively spirit is there, you can guess it would be very unlikely that someone would not welcome your greeting because all people under most circumstances would enjoy kind and cheerful expressions of friendship even from passing strangers.

But if greeting is interpreted by fellows as a show of piety, a value-laden imposition or a nuisance then you are basically sending the wrong message which is not the message of "salaam" which is about peace, sanity and good-faith.

Let me demonstrate this by a more cultural example. We in Iran know that in Islam we are supposed to say the Islamic greeting in full, i.e. "as salaam alaykum" which translates to "peace be upon you" instead of saying only "salaam" but sensitive Iranian Muslims may still intentionally drop "alaykum" because, at times, using it can be misinterpreted as a forceful show of piety than a heartfelt good wish for someone. So a good rule of thumb is that whether we can say the same Arabic thing in Persian without the pretentious pious connotations of saying it in Arabic and check to see whether the feeling of telling someone literally "Oh, Ali, peace be upon you today. How are you doing?" or "Oh, sir, peace be upon you. I have a question" sounds genuine to us or rather just redundant, slushy or artificial.

In fact we would rather try words that are not ideologically loaded at all to express a genuine friendly spirit like saying "Salaam Ali jan" (Hi, dear Ali) for a close friend, or "Salaam doost-e aziz" (literally, hello dear friend) for a warm stranger. Yes, we are not saying those specific Arabic words "salaam alaykum" but we are actually expressing the very spirit which Prophet Muhammad (pbuh) expected people when he recommend Arabs of his time to employ certain words to express greeting.

In other words, it was not the words per se that a supreme moral teacher like Muhammad (pbuh) was so concerned about but the spirit that they carried in the culture of his time.