property market slowdown

That's not how it works.  Shares bought back are effectively cancelled (see below*).  Subsequent changes in the price have no P&L effect.  There's an opportunity cost if the shares could have been bought more cheaply later, but no real loss. 

In exactly the same way, a company which issues shares may be considered to have suffered an opportunity cost if the share price goes up (because it could have issued the shares for more later), but you don't see that "cost" shown as a loss in the P&L.  Nor do you see a profit in the P&L if the value of the issued shares goes down!

* The following applies to UK companies.  The rules on when and how shares may be bought back may differ in other countries but the accounting should be the same:

• In the old days, all shares bought back were actually cancelled. There was a change in the law some years ago to allow shares to be bought into Treasury, which enables them to be reissued later.  This gives companies more flexibility, but they are still treated as cancelled for accounting and tax purposes.  Any reissue is treated for both accounting and tax as a new issue at the new price.
  
• Regardless of whether shares are cancelled when they are bought back, or bought into Treasury, the purchase must be paid for out of distributable profits, just like a dividend.  This reduces the amount available for future dividends.
• The main advantage of buying into Treasury is that, when the shares are reissued, the proceeds of the new issue are credited back to distributable profits (up to the amount of the debit when they were bought back), which enables the distributable profits to be reinstated.
  

"I hope that we both agree that after a share buyback the market cap of the company is the same - there are just less shares in circulation." - I don't think this is correct.  In a completely efficient market, when a company repurchases its own shares, it market capitalisation should fall by the amount paid for the shares.  Share buybacks are effectively a means of distribution and often used by companies to supplement normal distributions via dividend.  If the buyback is funded by a debt issue (or even just cash on the balance sheet), then the enterprise value of the company (ie market cap + debt - cash) will remain the same which is probably what you are referring to?

The fundamental balance sheet equation is that assets less liabilities equals shareholders equity.  In the past balance sheets were presented with assets and liabilities in the top half to give net assets equal to shareholder equity (share capital and reserves) in the bottom half.  The more fashionable presentation of a balance sheet is to show assets in the top half equalling liabilities and shareholder equity/funds (ie share capital and reserves) in the bottom half.  However, shareholder equity/funds should not be confused as a liability, it is merely a representation of the net asset value (assets less liabilities) ascribed to various classes of shareholders.

I find it easier to view the traditional presentation of the balance sheet where the net assets are shown on the top half of balance sheet and equivalent shareholder equity/funds on the bottom half.  When a share buyback is made, the reduction in cash will lead to its net assets falling (as will shareholder funds/equity in the bottom half of the balance sheet).  If company is valued at book value, then the fall in net assets represents the fall in market capitalisation equal to the buyback.

Perhaps the easier way to consider the effect of a share buyback on market capitalisation is thinking about what the shareholders have collectively before and after a buy back occurs.  For example, say there are 100 shareholders each with one share in a company that has net assets of £100 (say all in cash).  For simplicity assume the company is valued at book value, ie £100.  Before the buy back, shareholder hold 100 shares with a total book and market value of £100.  Now a buy back occurs whereby half the shares are bought back at par £1.  After the buy back, the shareholders collectively have £50 in cash and 50 shares worth £1 each (net assets of £50/50 shares).  The market value of the company has fallen from £100 to £50, equal to the cash paid out to repurchase the shares (shares are cancelled by the company on buyback).  So whilst the value per share remains unchanged, the total value of shares and hence capitalisation has reduced by the amount paid by the company to repurchase the shares. 

If you are arguing that market capitalisation per share should remain unchanged then I agree, but the total capitalisation will fall represented by the transfer of cash/value from the company to individual shareholders.