why do statistics that all money managers give you, show they
outperform all or most investment indices? who are on the other side
of the indices, underperforming?

The statistics are misleading to say the least.  They usually make a
bunch of investment suggestions.  Then they take their most profitable
suggestions by time period and string them together by time period to
show what you would have made if you put all your invested money in
just that series of most profitable investments at those particular
times.  And of course they ignore transaction fees or tax consequences
of buying and selling.  Then they compare them to more honest measures
of what other money managers earned.

Sometimes it is even worse, they will say they recommended buying
stock in Company A at, say, $20/share on mm/dd/yyyy and it rose to
$100/share on a given date maybe a year later.  Note they don't say
they recommended selling it then.

Another thing they do is choose the time period where they look the
best.  Be it the last one year, five years, ten years, etc.

You should take it with a grain of salt.

In the case of mutual funds, they cannot manipulate the numbers. 
Performance must be net of all fees.  See SEC Form N-1A.  So, they
must use accurate numbers, and the benchmarks they use do not relfect
any fees.

That being said, thereis no requirement as to the benchmark they use. 
Ihave seen bond funds compare themselves to the Lehman U.S treasury
index; (which as long as the economy doesn;t tank, will always have
better results).

Keep in mind, the market has been improving over the past 5 years.  If
you canmake aportfolio with a beta greater thanone, you should be able
to out do the S&P 500, the question is, what happens during a market
down turn.

What one must be very cautious about is the use of composites. 
Instead of showing you one fund they manages, they show you a slew of
them; unfortunaltely, the criteria is not always clear as to which
fundsone should include and which one should not.  (Theoretically, all
fund must be included except those that are materially different; orif
not different, there must be a representation that they are leaving
out a fund).

Well, of course, money managers provide statistics that seem to prove
that they are better than others or the market.

Ansel has suggested one method: picking the best of their past
recommendations  - or what they claim to have recommended.
There are so many statistics about financial investments, it is almost
always possible to find one that makes the manager's figures look
good.
As Ansel also mentions, choosing the period for the comparison can be
very "helpful".
For example, these days, a ten year view of stock value appreciation
might not be so attractive, whereas one for the last five years might
be good, since the market took a sharp decline early in 2000.
Or, they can compare with some average (Dow-Jones, industry, etc.),
finding one that makes them look good.