Why does increasing the money supply decrease the interest rate in layman's terms?

I will give a rather oversimplified finance side version (macroeconomic version requires a lot of details).

Generally new money is injected in the economy by the central bank by buying government bonds from the market. These bonds can be assumed to have a fixed coupon payment. The price of the bond in the secondary market is dynamic such that annual coupon payment per year ($c$) divided by current market price ($p_t$), gives the interest rate ($i_t$). Clearly, as $p_t$ increases, $i_t$ decreases and vice versa.

To inject more money, the central bank starts buying these bonds which pushes their price up and consequently decreases the rate of return on the bonds.

How does this affect other interest rates? Well all investment avenues are imperfect substitutes. So as rate of return on one decreases, so does that of others. Portfolio managers would divert investment to other asset classes and as their demand goes up, returns fall until a new equilibrium is established in which returns on most (if not all) assets are lower.

It should go up. More money means more inflation. Inflation requires higher interest rates to attract depositors who would otherwise spend the money before it lost more value.

There were times when people took any money they got and immediately went to spend it before it lost more value. Worst cases they had to use wheelbarrows to haul it to the store. Or they printed trillion dollar notes like zimbabwe did. So the velocity of money would go up and the interest rates would be sky high.

For you personally the money supply hurts you when it goes up as your money is worth less due to the law of supply and demand. With more money trying to buy same amount of goods prices will go up.

Here’s my Average Joe, fewest words, attempt: the more of a good circulating in the market, the less scarce is that good, and the lower the cost becomes. If money is the good, interest is the cost of borrowing.

When there’s not that much money on the market, in order for me to lend it to you, I have to re-allocate that money from a different place where it is being used (savings, investments, whatever). You, in turn, promise to pay me a bit more to convince me to do so (higher interest). As there’s not much money on the market being lent to people, you don’t have as many options so you’re willing to take on the higher costs.

When the money supply suddenly goes up, I can keep all my savings and investments where they are and still lend to you (but presumably, everyone else is also doing that) so to convince you to borrow from me, the rate I charge you has to goes down.

In an inflationary regime, money becomes one of the least valuable assets you can own. A ton of steel bought today will still be a ton of steel in a month, but the $750 that buys a ton of steel today won't be enough to buy a ton of steel next month. Assets have their own depreciation and costs of ownership, but the greater the rate of inflation is, the more attractive everything else looks compared to money.

Banks, of course, have piles of money, and they would like to charge as much interest as they can to lend it out (that's how they make money on money). But lending is a market; banks with lower rates will attract more borrowers, and banks with higher rates will attract fewer. So they cut their rates in order to attract borrowers who will hopefully invest their money in something, make a return, be able to afford to pay back their loan with interest, and make the bank at least a small profit. Whoever doesn't cut their rates is left sad and alone with a steadily devaluing pile of money. In a low-inflation or deflationary situation, the bank doesn't feel so bad about holding on to a pile of cash (or treasury bonds), so demand from borrowers is able to drive the interest rate up.