"Why is Bitcoin said to be scarce?"
Bitcoin is considered scarce primarily due to its built-in supply limit and the rules of its protocol. The maximum supply of Bitcoin is capped at 21 million coins. This scarcity is achieved through the process of mining, where miners solve complex mathematical puzzles to validate transactions and create new blocks on the blockchain.
Every four (4) years, an event known as the "halving" occurs in the Bitcoin network. During a halving, the block reward that miners receive for their efforts is reduced by half. This event is programmed into the Bitcoin protocol and occurs approximately every 210,000 blocks. As a result, the rate of new Bitcoin issuance decreases over time. The combination of the 21 million coin limit and the decreasing issuance rate due to halvings creates a scarcity effect, making Bitcoin increasingly difficult to mine and ultimately limiting its total supply.
This scarcity is in contrast to traditional fiat currencies, which can be printed by central banks without a fixed supply limit, potentially leading to inflation. Bitcoin's scarcity has contributed to its appeal as a digital store of value and a potential hedge against inflation.

"On addition of more coins to the already distributed 21 million coins will this change the halving graph of complex?, Will it alter the timing of halving in Bitcoin?"

The Bitcoin halving events are programmed into the Bitcoin protocol and occur automatically based on the block height, specifically every 210,000 blocks. This means that the halving schedule is determined by the consensus rules of the network and is not subject to arbitrary changes by individuals or entities. The protocol ensures that the halvings occur roughly every four years, but the exact timing may vary due to the unpredictable nature of block generation.
The halving events are designed to control the issuance of new bitcoins, gradually reducing the block reward and ultimately capping the total supply at 21 million coins. There is no provision within the protocol to extend or delay the halving events beyond the predetermined schedule.
Adding more available coins or changing the halving schedule would require a hard fork of the Bitcoin network, which would likely result in a split and the creation of a new blockchain. Such changes would require widespread consensus among the Bitcoin community, including miners, developers, users, and other stakeholders. Given the decentralized and consensus-driven nature of the Bitcoin network, making significant changes like altering the halving schedule is a complex process and would likely face significant resistance.

In summary, the proposed date of Bitcoin halving is determined by the protocol's rules and is not easily subject to delays or extensions. Any major changes to the halving schedule would require consensus among the Bitcoin community and would likely lead to a contentious fork of the network.

From the above I just got better understanding that even the man who invented Bitcoin has no monopolised power or single power to alter the trend of Bitcoin and halving period. It has to be consensus between many Bitcoin users .

I may not use the correct terms I'm still learning I hope this clarifies whatever confusion another may have concerning Bitcoin scarcity and how it relates to halving