explain why iv infusion of medication is the most dangerous method to administer medication
One of the reason is that the placement of an intravenous line requires breaking the skin and there is a risk of infection.
Intravenous therapy
As placement of an intravenous line requires breaking the skin, there is a risk of infection. 
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Intravenous therapy [SEP] Infection and inflammation
As placement of an intravenous line requires breaking the skin, there is a risk of infection. Skin-dwelling organisms such as coagulase-negative staphylococcus or "Candida albicans" may enter through the insertion site around the catheter, or bacteria may be accidentally introduced inside the catheter from contaminated equipment. Infection of an IV access site is usually local, causing easily visible swelling, redness, and fever. However, pathogens may also enter the bloodstream, causing an infection called sepsis which can be sudden and life-threatening. A central IV line poses a higher risk of sepsis, as it can deliver bacteria directly into the central circulation.