The short answer is no. There are many websites which advise people to stop eating vegetable oils and switch to fish oil in order to increase their intake of omega-3 fatty acids. Fish oil is a good source of omega-3 essential fatty acids and should be consumed, but that doesn’t necessarily mean that one should completely replace vegetable oils with fish oil.

Recent studies have shown that the consumption of fish oil (or, more specifically, the omega-3 fatty acids found in fish oil) can improve fertility in both men and women. DHA, which is a byproduct of omega-3 fatty acids, plays a key role in the mobility of sperm and health of sperm in men. Low blood levels of DHA have been linked to decreased fertility. Animal studies have found that the DHA in fish is vital to changing dysfunctional round-headed sperm into strong swimmers with cone-shaped heads packed with egg-opening proteins. (29)

A 2012 study involved children from 6 to 12 years of age with ADHD who were being treated with methylphenidate and standard behavior therapy for more than six months. The parents of these children reported no improvement in behavior and academic learning using these standard treatments. The researchers randomly gave some of the children an omega-3 and omega-6 acid supplementation or a placebo. They found “statistically significant improvement” for the omega group in the following categories: restlessness, aggressiveness, completing work and academic performance. (5)

Augood, C., Chakravarthy, U., Young, I., Vioque, J., de Jong, P. T., Bentham, G., Rahu, M., Seland, J., Soubrane, G., Tomazzoli, L., Topouzis, F., Vingerling, J. R., and Fletcher, A. E. Oily fish consumption, dietary docosahexaenoic acid and eicosapentaenoic acid intakes, and associations with neovascular age-related macular degeneration. Am J Clin Nutr 2008;88(2):398-406. View abstract.
Nine studies with 10 data sets used omega-3 PUFA dosages of less than 2000 mg/d.35,47,48,51,53,55,56,60,61 The main results revealed that there was no significant difference in the association of treatment with reduced anxiety symptoms between patients receiving omega-3 PUFA treatment and those not receiving it (k, 9; Hedges g, 0.457; 95% CI, –0.077 to 0.991; P = .09) (Figure 3B). Ten studies with 10 data sets used omega-3 PUFA dosages of at least 2000 mg/d.33,34,36,49,50,52,54,55,57-59 The main results revealed a significantly greater association of treatment with reduced anxiety symptoms in patients receiving omega-3 PUFA treatment than in those not receiving it (k, 11; Hedges g, 0.213; 95% CI, 0.031-0.395; P = .02) (Figure 3B). Furthermore, there was no significantly different estimated effect sizes between these 2 subgroups by the interaction test (P = .40).
Studies have also found that omega-3 fatty acids from fish oil are associated with improved survival rates for heart attack victims. A study published in the medical journal Circulation found that people who took a high dose of fish oil each for six months following the occurrence of a heart attack actually improved their hearts’ overall functioning and also reduced biomarkers of systemic inflammation. (20)
The deficiency of EPA and DHA in diet contributes to skin conditions, such as dandruff, thinning hair, eczema and psoriasis, as well as age spots and sun spots. Without the essential fatty acids, too much moisture leaves the skin. The truth is your internal health can appear on your skin, and taking fish oil internally as a supplement may be as good as or better than applying conventional moisturizers.

Omega-3s have been studied for other conditions, with either inconclusive or negative results. These conditions include allergies, atopic eczema (an allergic skin condition), cystic fibrosis, diabetes, inflammatory bowel diseases (Crohn’s disease or ulcerative colitis), intermittent claudication (a circulatory problem), nonalcoholic fatty liver disease, and osteoporosis. 
When taking fish oil, more is not always better. Remember that you want it to stay in a balanced ratio with omega-6 fats. For most people, I recommend a 1,000-milligram dose of fish oil daily as a good amount and the most scientifically studied dosage. I highly recommend not taking more than that unless directed to under the supervision of a doctor.
To exclude the possible confounding effects of clinical variables on the Hedges g, metaregression analysis was conducted with an unrestricted maximum likelihood random-effects model of single variables when there were more than 10 data sets available. Specifically, the clinical variables of interest included mean age, female proportion, sample size, mean body mass index, daily omega-3 PUFA dosage, EPA to DHA ratio, treatment duration, dropout rate, and others. In addition, a subgroup meta-analysis was conducted to investigate potential sources of heterogeneity, specifically, a further subgroup meta-analysis focused on those trials that were placebo controlled or non–placebo controlled. To more clearly uncover the differences in the meta-analysis results among the recruited studies, a further subgroup meta-analysis was performed according to the presence of a specific clinical diagnosis or no specific clinical condition, mean omega-3 PUFA daily dosage, and mean age. In addition, in a previous study, the EPA percentage (ie, ≥60%) in the PUFA regimens had different effects on depression treatment.9 Therefore, we also arranged the subgroup meta-analysis based on the EPA percentage. Furthermore, we arranged subgroup meta-analysis procedures only when there were at least 3 data sets included.45 To investigate the potentially different estimated effect sizes between subgroups, we performed an interaction test and calculated the corresponding P values.46
The bottom line of all that is that there was no clear health benefit from consuming omega-3 fatty acids in food or supplements. There was a suggestion of a possible benefit from LCn3 on cardiac events, but this did not hold up when they took into consideration the quality of the evidence. The better trials, with less risk of bias, tended to be negative.

Despite this one study, you should still consider eating fish and other seafood as a healthy strategy. If we could absolutely, positively say that the benefits of eating seafood comes entirely from omega-3 fats, then downing fish oil pills would be an alternative to eating fish. But it’s more than likely that you need the entire orchestra of fish fats, vitamins, minerals, and supporting molecules, rather than the lone notes of EPA and DHA.
In recent years, many people – particularly those who strictly follow a vegetarian or vegan diet – have believed that they do not have to consume animal products to get omega-3s, as long as they are consuming high amounts of plant-based omega-3s. But, as I mentioned before, most of the health benefits that you can get from omega-3 fats are linked to animal-based EPA and DHA fats – not plant-based ALA. They are simply NOT interchangeable.

A certain kidney disease called IgA nephropathy. Some research shows that long-term but not short-term use of fish oil can slow the loss of kidney function in high-risk patients with IgA nephropathy. Fish oil might have greater effects when taken at higher doses. Also, it might be most effective in people with IgA nephropathy who have higher levels of protein in the urine.