Perhaps what is counter-intuitive is the fact that whenever $A$ is false, then $A\Rightarrow B$ is true, based on how logical implication is defined: $$ \begin{array}{|c|c|c|} \hline A & B & A\Rightarrow B \\ \hline {\bf F} & F & {\bf T}\\ {\bf F} & T & {\bf T}\\ T & F & F\\ T & T & T\\ \hline \end{array} $$

Applied to the example of the coin:

if the coin shows heads, then it shows tails
                     or
if the coin shows tails, then it shows heads

Let's say we flip a coin, and it shows heads.

Then then the following statement is false:

the coin shows tails

and thus the second half of the disjunction is true:

if the coin shows tails, then it shows heads

and thus the whole disjunction is true.

Same goes for if tails were shown.

Perhaps what is counter-intuitive is the fact that whenever $A$ is false, then $A\Rightarrow B$ is true, based on how logical implication is defined: $$ \begin{array}{|c|c|c|} \hline A & B & A\Rightarrow B \\ \hline {\bf F} & F & {\bf T}\\ {\bf F} & T & {\bf T}\\ T & F & F\\ T & T & T\\ \hline \end{array} $$

Applied to the example of the coin:

if the coin shows heads, then it shows tails
                     or
if the coin shows tails, then it shows heads

Let's say a coin is flipped, and it shows heads.

Then the following statement is false:

the coin shows tails

and thus the second half of the disjunction is true:

if the coin shows tails, then it shows heads

therefore the whole disjunction is true.

Similarly if tails were shown.