Why is screening test more concerned about sensitivity while diagnostic test is more concerned about specificity? 
*

*Screening Test : A large number of apparently healthy people are tested to identify those who are at a risk of the condition or disease. 

*Diagnostic Test : When we get a screen positive individual or showing symptoms , we are interested to determine which condition or disease is responsible for such symptoms. Thus we perform a diagnostic test.

*Sensitivity : probability that a person with the condition will be classified in one's study as having the condition.

*Specificity : probability that a person without the condition will be classified in one's study as being without the condition.
I have not understood the statement from wikipedia :
" overdiagnosis, misdiagnosis, and creating a false sense of security are some potential adverse effects of screening. For these reasons, a test used in a screening program, especially for a disease with low incidence, must have good sensitivity in addition to acceptable specificity."
As far i can apply common sense for why screening test is more concerned  about sensitivity is that , it is necessary to identify the people having the condition to minimize the risk or to prevent the condition. But what does wikipedia  want to mean by 

overdiagnosis, misdiagnosis, and creating a false sense of security are some potential adverse effects of screening.Those are the reasons for why screening test is more concerned  about sensitivity.

And the  second and last question is 


*

*why is diagnostic test  more concerned  about specificity ?


As i perform a diagnostic test when i get the symptom or positive screening test , then why do i need good specificity? Is that for , perhaps my study is on cancer and an individual have some symptoms but the symptoms can be for another disease except cancer. So if i can identify the individual that s/he has not cancer, s/he will not be carried out for further experiment in my study. So that diagnostic testing is more concerned about specificity. 
Do my logic make sense ?
 A: A diagnostic test is used to decide whether a patient requires treatment/surgery/whatever intervention. False positives are particularly undesirable because what comes next is often costly, potentially dangerous for the patient (both physically and psychologically) and can significantly reduce quality of life.
Imagine cutting off someone's leg only to later find out it wasn't necessary. Patients generally don't appreciate 'Oops, my bad' in such occasions. Such dramas ruin lives, for both the patient and the physician (many have lost their license due to related lawsuits).

overdiagnosis, misdiagnosis, and creating a false sense of security are some potential adverse effects of screening.Those are the reasons for why screening test is more concerned about sensitivity.

This wikipedia quote is quite unfortunate. Overdiagnosis and misdiagnosis are both consequences of high false positive rate (false positive rate increases along with sensitivity). Creating a false sense of security is the only valid reason to maximize sensitivity in that list. The main point of screening is secondary prevention, which starts by identifying all patients with (signs of) a given condition; preferably with few false positives but this is only a secondary criterion.
